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#include<deque>
#include<string>
#include<vector>
#include<complex>
#include<assert.h>
#include<algorithm>
#define PI 3.14159265358979323846
void fft(std::vector<std::complex<double>>&a, bool invert)
{
    for (int i = 1, j = 0; i < a.size(); i++)
    {
        int bit = int(a.size()) >> 1;
        for (; j & bit; bit >>= 1)
        {
            j ^= bit;
        }
        j ^= bit;
        if (i < j)
        {
            swap(a[i], a[j]);
        }
    }
    for (int len = 2; len <= a.size(); len <<= 1)
    {
        double ang = 2 * PI / len * (invert ? -1 : 1);
        std::complex<double>wlen(cos(ang), sin(ang));
        for (int i = 0; i < a.size(); i += len)
        {
            std::complex<double>w(1);
            for (int j = 0; j < (len >> 1); j++)
            {
                std::complex<double>u = a[i + j], v = a[i + j + (len >> 1)] * w;
                a[i + j] = u + v;
                a[i + j + (len >> 1)] = u - v;
                w *= wlen;
            }
        }
    }
    if (invert)
    {
        for (int i = 0; i < a.size(); i++)
        {
            a[i] /= a.size();
        }
    }
}
struct BigInt
{
    bool is_negative = false;
    std::deque<int>Digits = { 0 };
    BigInt() { }
    template<typename T>
    BigInt(T number)
    {
        (*this) = number;
    }
    inline operator std::string() const
    {
        std::stringstream string_stream;
        string_stream << *this;
        return string_stream.str();
    }
    inline operator bool() const
    {
        return *this != 0;
    }
    inline operator int32_t() const
    {
        return std::stoi(*this);
    }
    inline operator int64_t() const
    {
        return std::stoll(*this);
    }
    inline operator unsigned() const
    {
        return std::stoul(*this);
    }
    inline operator double() const
    {
        return std::stod(*this);
    }
    inline operator float() const
    {
        return std::stof(*this);
    }
    inline operator char() const
    {
        return int(*this);
    }
    inline void shrink_to_fit()
    {
        int new_size = Digits.size();
        while (new_size > 1 && Digits[new_size - 1] == 0)
        {
            new_size--;
        }
        Digits.resize(new_size);
    }
    inline friend std::istream& operator >> (std::istream& input_stream, BigInt& object)
    {
        std::string number;
        input_stream >> number;
        object = number;
        return input_stream;
    }
    friend std::ostream& operator << (std::ostream& output_stream, BigInt object)
    {
        object.shrink_to_fit();
        if (object.is_negative && (object.Digits.size() != 1 || object.Digits[0] != 0))
        {
            output_stream << '-';
        }
        bool leading_zeros = true;
        for (int i = object.Digits.size() - 1; i >= 0; i--)
        {
            leading_zeros &= !object.Digits[i];
            if (object.Digits[i] || !leading_zeros)
            {
                output_stream << object.Digits[i];
            }
        }
        if (leading_zeros)
        {
            output_stream << '0';
        }
        return output_stream;
    }
    BigInt& operator = (std::string number)
    {
        if (number[0] == '-')
        {
            is_negative = true;
        }
        else
        {
            is_negative = false;
        }
        Digits.resize(number.size());
        int number_size = number.size();
        while (number.size() > is_negative)
        {
            if (number.back() != '.')
            {
                Digits[number_size - number.size()] = number.back() - '0';
            }
            else
            {
                number.pop_back();
                *this = number;
                return *this;
            }
            number.pop_back();
        }
        if (number.size())
        {
            Digits.pop_back();
        }
        return *this;
    }
    template<typename T>
    inline BigInt& operator = (T number)
    {
        std::stringstream string_stream;
        string_stream << std::fixed << number;
        *this = string_stream.str();
        return *this;
    }
    friend bool operator > (BigInt first_object, BigInt second_object)
    {
        if (first_object.is_negative)
        {
            if (second_object.is_negative)
            {
                first_object.is_negative = false;
                second_object.is_negative = false;
                return first_object < second_object;
            }
            else
            {
                return false;
            }
        }
        else if (second_object.is_negative)
        {
            return true;
        }
        if (first_object.Digits.size() < second_object.Digits.size())
        {
            first_object.Digits.resize(second_object.Digits.size());
        }
        else if (first_object.Digits.size() > second_object.Digits.size())
        {
            second_object.Digits.resize(first_object.Digits.size());
        }
        for (int i = first_object.Digits.size() - 1; i >= 0; i--)
        {
            if (first_object.Digits[i] < second_object.Digits[i])
            {
                return false;
            }
            else if (first_object.Digits[i] > second_object.Digits[i])
            {
                return true;
            }
        }
        return false;
    }
    friend bool operator < (BigInt first_object, BigInt second_object)
    {
        if (first_object.is_negative)
        {
            if (second_object.is_negative)
            {
                first_object.is_negative = false;
                second_object.is_negative = false;
                return first_object > second_object;
            }
            else
            {
                return true;
            }
        }
        else if (second_object.is_negative)
        {
            return false;
        }
        if (first_object.Digits.size() < second_object.Digits.size())
        {
            first_object.Digits.resize(second_object.Digits.size());
        }
        else if (first_object.Digits.size() > second_object.Digits.size())
        {
            second_object.Digits.resize(first_object.Digits.size());
        }
        for (int i = first_object.Digits.size() - 1; i >= 0; i--)
        {
            if (first_object.Digits[i] < second_object.Digits[i])
            {
                return true;
            }
            else if (first_object.Digits[i] > second_object.Digits[i])
            {
                return false;
            }
        }
        return false;
    }
    friend bool operator == (BigInt first_object, BigInt second_object)
    {
        if (first_object.Digits.size() < second_object.Digits.size())
        {
            first_object.Digits.resize(second_object.Digits.size());
        }
        else if (first_object.Digits.size() > second_object.Digits.size())
        {
            second_object.Digits.resize(first_object.Digits.size());
        }
        if (first_object.Digits == second_object.Digits)
        {
            first_object.shrink_to_fit();
            second_object.shrink_to_fit();
            return (!(first_object.is_negative ^ second_object.is_negative) || (first_object.Digits.size() == 1 && first_object.Digits[0] == 0));
        }
        else
        {
            return false;
        }
    }
    inline friend bool operator >= (BigInt first_object, BigInt second_object)
    {
        return first_object > second_object || first_object == second_object;
    }
    inline friend bool operator <= (BigInt first_object, BigInt second_object)
    {
        return first_object < second_object || first_object == second_object;
    }
    inline friend bool operator != (BigInt first_object, BigInt second_object)
    {
        return !(first_object == second_object);
    }
    template<typename T>
    inline friend bool operator > (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object > second_object;
    }
    template<typename T>
    inline friend bool operator < (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object < second_object;
    }
    template<typename T>
    inline friend bool operator == (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object == second_object;
    }
    template<typename T>
    inline friend bool operator >= (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object >= second_object;
    }
    template<typename T>
    inline friend bool operator <= (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object <= second_object;
    }
    template<typename T>
    inline friend bool operator != (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object != second_object;
    }
    template<typename T>
    inline friend bool operator > (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object > second_object;
    }
    template<typename T>
    inline friend bool operator < (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object < second_object;
    }
    template<typename T>
    inline friend bool operator == (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object == second_object;
    }
    template<typename T>
    inline friend bool operator >= (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object >= second_object;
    }
    template<typename T>
    inline friend bool operator <= (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object <= second_object;
    }
    template<typename T>
    inline friend bool operator != (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object != second_object;
    }
    friend BigInt operator + (BigInt first_object, BigInt second_object)
    {
        if (second_object.is_negative)
        {
            second_object.is_negative = false;
            return first_object - second_object;
        }
        if (first_object.is_negative)
        {
            first_object.is_negative = false;
            return second_object - first_object;
        }
        int carry = 0;
        if (first_object.Digits.size() < second_object.Digits.size())
        {
            first_object.Digits.resize(second_object.Digits.size());
        }
        if (first_object.Digits.size() > second_object.Digits.size())
        {
            second_object.Digits.resize(first_object.Digits.size());
        }
        for (int i = 0; i < first_object.Digits.size() - 1; i++)
        {
            first_object.Digits[i] += carry + second_object.Digits[i];
            carry = first_object.Digits[i] / 10;
            first_object.Digits[i] %= 10;
        }
        first_object.Digits[first_object.Digits.size() - 1] += carry;
        first_object.shrink_to_fit();
        return first_object;
    }
    friend BigInt operator - (BigInt first_object, BigInt second_object)
    {
        if (second_object.is_negative)
        {
            second_object.is_negative = false;
            return first_object + second_object;
        }
        if (first_object < second_object)
        {
            first_object = second_object - first_object;
            first_object.is_negative = !first_object.is_negative;
            return first_object;
        }
        bool borrow = false;
        second_object.Digits.resize(first_object.Digits.size());
        for (int i = 0; i < first_object.Digits.size(); i++)
        {
            first_object.Digits[i] -= second_object.Digits[i] + borrow;
            if (first_object.Digits[i] < 0)
            {
                first_object.Digits[i] += 10;
                borrow = true;
            }
            else
            {
                borrow = false;
            }
        }
        first_object.shrink_to_fit();
        return first_object;
    }
    friend BigInt operator * (BigInt first_object, BigInt second_object)
    {
        if (first_object.Digits.size() * second_object.Digits.size() <= (first_object.Digits.size() + second_object.Digits.size()) * log2(first_object.Digits.size() + second_object.Digits.size()))
        {
            BigInt result;
            result.Digits.resize(first_object.Digits.size() + second_object.Digits.size());
            for (int i = 0; i < second_object.Digits.size(); i++)
            {
                int carry = 0;
                for (int j = 0; j < first_object.Digits.size(); j++)
                {
                    result.Digits[i + j] += first_object.Digits[j] * second_object.Digits[i] + carry;
                    carry = result.Digits[i + j] / 10;
                    result.Digits[i + j] %= 10;
                }
                result.Digits[i + first_object.Digits.size()] = carry;
            }
            result.shrink_to_fit();
            result.is_negative = first_object.is_negative ^ second_object.is_negative;
            return result;
        }
        first_object.is_negative ^= second_object.is_negative;
        int new_size = 1;
        while (new_size < first_object.Digits.size() + second_object.Digits.size())
        {
            new_size <<= 1;
        }
        first_object.Digits.resize(new_size);
        second_object.Digits.resize(new_size);
        std::vector<std::complex<double>>fa(first_object.Digits.begin(), first_object.Digits.end()), fb(second_object.Digits.begin(), second_object.Digits.end());
        fft(fa, false);
        fft(fb, false);
        for (int i = 0; i < new_size; i++)
        {
            fa[i] *= fb[i];
        }
        fft(fa, true);
        for (int i = 0; i < new_size; i++)
        {
            first_object.Digits[i] = round(fa[i].real());
        }
        int carry = 0;
        for (int i = 0; i < new_size; i++)
        {
            first_object.Digits[i] += carry;
            carry = first_object.Digits[i] / 10;
            first_object.Digits[i] %= 10;
        }
        first_object.shrink_to_fit();
        return first_object;
    }
    friend BigInt operator / (BigInt first_object, BigInt second_object)
    {
        assert(second_object != 0);
        BigInt result, carry;
        result.is_negative = first_object.is_negative ^ second_object.is_negative;
        first_object.is_negative = false;
        second_object.is_negative = false;
        carry.Digits.resize(first_object.Digits.size());
        result.Digits.resize(first_object.Digits.size());
        for (int i = first_object.Digits.size() - 1; i >= 0; i--)
        {
            carry.Digits.push_front(first_object.Digits[i]);
            int answer = 9;
            BigInt temp = second_object * 9;
            while (answer >= 0)
            {
                if (temp <= carry)
                {
                    break;
                }
                temp -= second_object;
                answer--;
            }
            result.Digits[i] = answer;
            carry -= second_object * answer;
        }
        result.shrink_to_fit();
        return result;
    }
    friend BigInt operator % (BigInt first_object, BigInt second_object)
    {
        assert(second_object != 0);
        BigInt result, carry;
        bool negative_temp = first_object.is_negative;
        first_object.is_negative = false;
        second_object.is_negative = false;
        carry.Digits.resize(first_object.Digits.size());
        result.Digits.resize(first_object.Digits.size());
        for (int i = first_object.Digits.size() - 1; i >= 0; i--)
        {
            carry.Digits.push_front(first_object.Digits[i]);
            int answer = 9;
            BigInt temp = second_object * 9;
            while (answer >= 0)
            {
                if (temp <= carry)
                {
                    break;
                }
                temp -= second_object;
                answer--;
            }
            result.Digits[i] = answer;
            carry -= second_object * answer;
        }
        carry.is_negative = negative_temp;
        carry.shrink_to_fit();
        return carry;
    }
    friend BigInt operator | (BigInt first_object, BigInt second_object)
    {
        if (first_object.is_negative)
        {
            return ~(~first_object & ~second_object);
        }
        bool flip = false;
        if (second_object.is_negative)
        {
            flip = true;
            second_object = ~second_object;
        }
        std::string first_number, second_number;
        while (first_object)
        {
            int64_t block = first_object % (1 << 30);
            first_object /= (1 << 30);
            for (int i = 0; i < 30; i++)
            {
                if (!block && !first_object)
                {
                    break;
                }
                first_number.push_back((block % 2) + '0');
                block /= 2;
            }
        }
        while (second_object)
        {
            int64_t block = second_object % (1 << 30);
            second_object /= (1 << 30);
            for (int i = 0; i < 30; i++)
            {
                if (!block && !second_object)
                {
                    break;
                }
                second_number.push_back((block % 2) + '0');
                block /= 2;
            }
        }
        first_number.push_back('0');
        second_number.push_back('0');
        while (first_number.size() < second_number.size())
        {
            first_number.push_back('0');
        }
        while (first_number.size() > second_number.size())
        {
            second_number.push_back('0');
        }
        if (flip)
        {
            for (int i = 0; i < second_number.size(); i++)
            {
                if (second_number[i] == '0')
                {
                    second_number[i] = '1';
                }
                else
                {
                    second_number[i] = '0';
                }
            }
        }
        for (int i = 0; i < first_number.size(); i++)
        {
            first_number[i] = ((first_number[i] - '0') || (second_number[i] - '0')) + '0';
        }
        if (first_number.back() - '0')
        {
            flip = true;
            for (int i = 0; i < first_number.size(); i++)
            {
                if (first_number[i] == '0')
                {
                    first_number[i] = '1';
                }
                else
                {
                    first_number[i] = '0';
                }
            }
        }
        else
        {
            flip = false;
        }
        BigInt answer, temp = 1;
        reverse(first_number.begin(), first_number.end());
        while (first_number.size())
        {
            if (first_number.back() - '0')
            {
                answer += temp;
            }
            temp += temp;
            first_number.pop_back();
        }
        if (flip)
        {
            return ~answer;
        }
        return answer;
    }
    friend BigInt operator & (BigInt first_object, BigInt second_object)
    {
        if (first_object.is_negative)
        {
            return ~(~first_object | ~second_object);
        }
        bool flip = false;
        if (second_object.is_negative)
        {
            flip = true;
            second_object = ~second_object;
        }
        std::string first_number, second_number;
        while (first_object)
        {
            int64_t block = first_object % (1 << 30);
            first_object /= (1 << 30);
            for (int i = 0; i < 30; i++)
            {
                if (!block && !first_object)
                {
                    break;
                }
                first_number.push_back((block % 2) + '0');
                block /= 2;
            }
        }
        while (second_object)
        {
            int64_t block = second_object % (1 << 30);
            second_object /= (1 << 30);
            for (int i = 0; i < 30; i++)
            {
                if (!block && !second_object)
                {
                    break;
                }
                second_number.push_back((block % 2) + '0');
                block /= 2;
            }
        }
        first_number.push_back('0');
        second_number.push_back('0');
        while (first_number.size() < second_number.size())
        {
            first_number.push_back('0');
        }
        while (first_number.size() > second_number.size())
        {
            second_number.push_back('0');
        }
        if (flip)
        {
            for (int i = 0; i < second_number.size(); i++)
            {
                if (second_number[i] == '0')
                {
                    second_number[i] = '1';
                }
                else
                {
                    second_number[i] = '0';
                }
            }
        }
        for (int i = 0; i < first_number.size(); i++)
        {
            first_number[i] = ((first_number[i] - '0') && (second_number[i] - '0')) + '0';
        }
        if (first_number.back() - '0')
        {
            flip = true;
            for (int i = 0; i < first_number.size(); i++)
            {
                if (first_number[i] == '0')
                {
                    first_number[i] = '1';
                }
                else
                {
                    first_number[i] = '0';
                }
            }
        }
        else
        {
            flip = false;
        }
        BigInt answer, temp = 1;
        reverse(first_number.begin(), first_number.end());
        while (first_number.size())
        {
            if (first_number.back() - '0')
            {
                answer += temp;
            }
            temp += temp;
            first_number.pop_back();
        }
        if (flip)
        {
            return ~answer;
        }
        return answer;
    }
    friend BigInt operator ^ (BigInt first_object, BigInt second_object)
    {
        if (first_object == 0)
        {
            return second_object;
        }
        if (second_object == 0)
        {
            return first_object;
        }
        if (first_object < 0 && second_object < 0)
        {
            return ~first_object ^ ~second_object;
        }
        if (first_object < 0)
        {
            return ~(~first_object ^ second_object);
        }
        if (second_object < 0)
        {
            return ~(first_object ^ ~second_object);
        }
        std::string first_number, second_number;
        while (first_object)
        {
            int64_t block = first_object % (1 << 30);
            first_object /= (1 << 30);
            for (int i = 0; i < 30; i++)
            {
                if (!block && !first_object)
                {
                    break;
                }
                first_number.push_back((block % 2) + '0');
                block /= 2;
            }
        }
        while (second_object)
        {
            int64_t block = second_object % (1 << 30);
            second_object /= (1 << 30);
            for (int i = 0; i < 30; i++)
            {
                if (!block && !second_object)
                {
                    break;
                }
                second_number.push_back((block % 2) + '0');
                block /= 2;
            }
        }
        while (first_number.size() < second_number.size())
        {
            first_number.push_back('0');
        }
        while (first_number.size() > second_number.size())
        {
            second_number.push_back('0');
        }
        for (int i = 0; i < first_number.size(); i++)
        {
            first_number[i] = ((first_number[i] - '0') ^ (second_number[i] - '0')) + '0';
        }
        reverse(first_number.begin(), first_number.end());
        BigInt answer, temp = 1;
        while (first_number.size())
        {
            if (first_number.back() - '0')
            {
                answer += temp;
            }
            temp += temp;
            first_number.pop_back();
        }
        return answer;
    }
    friend BigInt operator >> (BigInt object, int number)
    {
        if (number < 0)
        {
            return object << -number;
        }
        if (object.is_negative)
        {
            return ~(~object >> number);
        }
        std::string bits;
        while (object)
        {
            int64_t block = object % (1 << 30);
            object /= (1 << 30);
            for (int i = 0; i < 30; i++)
            {
                if (!block && !object)
                {
                    break;
                }
                bits.push_back((block % 2) + '0');
                block /= 2;
            }
        }
        reverse(bits.begin(), bits.end());
        bits.resize((number > bits.size() ? 0 : bits.size() - number));
        BigInt answer, temp = 1;
        while (bits.size())
        {
            if (bits.back() - '0')
            {
                answer += temp;
            }
            temp += temp;
            bits.pop_back();
        }
        return answer;
    }
    friend BigInt operator << (BigInt object, int number)
    {
        if (number == 0)
        {
            return object;
        }
        else if (number < 0)
        {
            return object >> -number;
        }
        std::string bits;
        bool negative_temp = object.is_negative;
        object.is_negative = false;
        while (object)
        {
            int64_t block = object % (1 << 30);
            object /= (1 << 30);
            for (int i = 0; i < 30; i++)
            {
                if (!block && !object)
                {
                    break;
                }
                bits.push_back((block % 2) + '0');
                block /= 2;
            }
        }
        reverse(bits.begin(), bits.end());
        while (number--)
        {
            bits.push_back('0');
        }
        BigInt answer, temp = 1;
        while (bits.size())
        {
            if (bits.back() - '0')
            {
                answer += temp;
            }
            temp += temp;
            bits.pop_back();
        }
        answer.is_negative = negative_temp;
        return answer;
    }
    template<typename T>
    inline friend BigInt operator + (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object + second_object;
    }
    template<typename T>
    inline friend BigInt operator - (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object - second_object;
    }
    template<typename T>
    inline friend BigInt operator * (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object * second_object;
    }
    template<typename T>
    inline friend BigInt operator / (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object / second_object;
    }
    template<typename T>
    inline friend BigInt operator % (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object % second_object;
    }
    template<typename T>
    inline friend BigInt operator | (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object | second_object;
    }
    template<typename T>
    inline friend BigInt operator & (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object & second_object;
    }
    template<typename T>
    inline friend BigInt operator ^ (BigInt first_object, T number)
    {
        BigInt second_object;
        second_object = number;
        return first_object ^ second_object;
    }
    template<typename T>
    inline friend BigInt operator + (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object + second_object;
    }
    template<typename T>
    inline friend BigInt operator - (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object - second_object;
    }
    template<typename T>
    inline friend BigInt operator * (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object * second_object;
    }
    template<typename T>
    inline friend BigInt operator / (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object / second_object;
    }
    template<typename T>
    inline friend BigInt operator % (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object % second_object;
    }
    template<typename T>
    inline friend BigInt operator | (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object | second_object;
    }
    template<typename T>
    inline friend BigInt operator & (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object & second_object;
    }
    template<typename T>
    inline friend BigInt operator ^ (T number, BigInt second_object)
    {
        BigInt first_object;
        first_object = number;
        return first_object ^ second_object;
    }
    template<typename T>
    inline BigInt& operator += (T number)
    {
        *this = *this + number;
        return *this;
    }
    template<typename T>
    inline BigInt& operator -= (T number)
    {
        *this = *this - number;
        return *this;
    }
    template<typename T>
    inline BigInt& operator *= (T number)
    {
        *this = *this * number;
        return *this;
    }
    template<typename T>
    inline BigInt& operator /= (T number)
    {
        *this = *this / number;
        return *this;
    }
    template<typename T>
    inline BigInt& operator %= (T number)
    {
        *this = *this % number;
        return *this;
    }
    template<typename T>
    inline BigInt& operator |= (T number)
    {
        *this = *this | number;
        return *this;
    }
    template<typename T>
    inline BigInt& operator &= (T number)
    {
        *this = *this & number;
        return *this;
    }
    template<typename T>
    inline BigInt& operator ^= (T number)
    {
        *this = *this ^ number;
        return *this;
    }
    inline BigInt& operator >>= (int number)
    {
        *this = *this >> number;
        return *this;
    }
    inline BigInt& operator <<= (int number)
    {
        *this = *this << number;
        return *this;
    }
    inline BigInt& operator ++ ()
    {
        (*this) = (*this) + 1;
        return (*this);
    }
    inline BigInt operator ++ (int32_t)
    {
        (*this) = (*this) + 1;
        return (*this) - 1;
    }
    inline BigInt& operator -- ()
    {
        (*this) = (*this) - 1;
        return (*this);
    }
    inline BigInt operator -- (int32_t)
    {
        (*this) = (*this) - 1;
        return (*this) + 1;
    }
    inline friend BigInt operator - (BigInt object)
    {
        return 0 - object;
    }
    inline BigInt operator ~ ()
    {
        return  0 - (*this) - 1;
    }
};
BigInt __gcd(BigInt first_number, BigInt second_number)
{
    return second_number == 0 ? first_number : __gcd(second_number, first_number % second_number);
}
inline BigInt __lcm(BigInt first_number, BigInt second_number)
{
    return first_number * second_number / __gcd(first_number, second_number);
}
BigInt phi(BigInt number)
{
    BigInt answer = number;
    for (BigInt i = 2; i * i <= number; i++)
    {
        if (number % i == 0)
        {
            while (number % i == 0)
            {
                number /= i;
            }
            answer -= answer / i;
        }
    }
    if (number > 1)
    {
        answer -= answer / number;
    }
    return answer;
}
int phi(int number)
{
    int answer = number;
    for (int i = 2; i * i <= number; i += 1)
    {
        if (number % i == 0)
        {
            while (number % i == 0)
            {
                number /= i;
            }
            answer -= answer / i;
        }
    }
    if (number > 1)
    {
        answer -= answer / number;
    }
    return answer;
}
inline BigInt abs(BigInt number)
{
    number.is_negative = false;
    return number;
}
class BigFloat
{
private :
    BigInt Numerator, Denominator;
public :
    BigFloat() { }
    template<typename T>
    BigFloat(T number)
    {
        (*this) = number;
    }
    inline operator bool() const
    {
        return *this != 0;
    }
    inline operator int() const
    {
        return Numerator / Denominator;
    }
    inline operator unsigned() const
    {
        return Numerator / Denominator;
    }
    inline operator double()
    {
        return stod((*this).str(15));
    }
    inline operator float()
    {
        return stof((*this).str(7));
    }
    inline operator char() const
    {
        return int(*this);
    }
    inline operator BigInt() const
    {
        return Numerator / Denominator;
    }
    inline BigInt numerator()
    {
        return Numerator;
    }
    inline BigInt denominator()
    {
        return Denominator;
    }
    inline void numerator(BigInt number)
    {
        Numerator = number;
        (*this).shrink_to_fit();
    }
    inline void denominator(BigInt number)
    {
        Denominator = number;
        (*this).shrink_to_fit();
    }
    template<typename T>
    inline void numerator(T number)
    {
        Numerator = number;
        (*this).shrink_to_fit();
    }
    template<typename T>
    inline void denominator(T number)
    {
        Denominator = number;
        (*this).shrink_to_fit();
    }
    inline void shrink_to_fit()
    {
        Numerator.is_negative ^= Denominator.is_negative;
        Denominator.is_negative = false;
        if (Denominator.Digits.size() >= 1000)
        {
            BigInt GCD = __gcd(Numerator, Denominator);
            Numerator /= GCD;
            Denominator /= GCD;
        }
    }
    std::string str(int Digits = 0)
    {
        if (Denominator == 0)
        {
            return "inf";
        }
        std::string answer;
        bool negative_temp = false;
        BigInt numerator = Numerator, denominator = Denominator;
        if (numerator.is_negative ^ denominator.is_negative)
        {
            negative_temp = true;
        }
        numerator.is_negative = false;
        denominator.is_negative = false;
        for (int i = 0; i < Digits; i++)
        {
            numerator.Digits.push_front(0);
        }
        numerator /= denominator;
        for (int i = Digits; i < numerator.Digits.size(); i++)
        {
            answer.push_back(numerator.Digits[i] + '0');
        }
        if (Digits >= numerator.Digits.size())
        {
            answer.push_back('0');
        }
        if (negative_temp)
        {
            answer.push_back('-');
        }
        reverse(answer.begin(), answer.end());
        if (Digits)
        {
            answer.push_back('.');
            std::string temp;
            for (int i = 0; i < Digits; i++)
            {
                temp.push_back(numerator.Digits[i] + '0');
            }
            reverse(temp.begin(), temp.end());
            for (int i = temp.size(); i < Digits; i++)
            {
                answer.push_back('0');
            }
            answer += temp;
        }
        return answer;
    }
    inline friend std::istream& operator >> (std::istream& input_stream, BigFloat& object)
    {
        std::string number;
        input_stream >> number;
        object = number;
        return input_stream;
    }
    friend std::ostream& operator << (std::ostream& output_stream, BigFloat object)
    {
        if (object.Denominator == 0)
        {
            if (object.Numerator == 0)
            {
                output_stream << "Undefined";
                return output_stream;
            }
            else
            {
                output_stream << "inf";
                return output_stream;
            }
        }
        BigInt GCD = __gcd(object.Numerator, object.Denominator);
        object.Numerator /= GCD;
        object.Denominator /= GCD;
        output_stream << std::fixed << object.Numerator << '/' << object.Denominator;
        return output_stream;
    }
    BigFloat& operator = (std::string number)
    {
        if (number[0] == '-')
        {
            Numerator.is_negative = true;
        }
        int dot_place = 0;
        Numerator.Digits.resize(number.size());
        Numerator.Digits[number.size() - 1] = 0;
        for (int i = number.size() - 1; i >= Numerator.is_negative; i--)
        {
            if (number[i] != '.')
            {
                Numerator.Digits[number.size() - i - (bool)dot_place - 1] = number[i] - '0';
            }
            else
            {
                dot_place = number.size() - i - 1;
            }
        }
        if (dot_place)
        {
            Numerator.Digits.pop_back();
        }
        Denominator.Digits = std::deque<int>(dot_place + 1);
        Denominator.Digits[dot_place] = 1;
        (*this).shrink_to_fit();
        return *this;
    }
    template<typename T>
    inline BigFloat& operator = (T number)
    {
        std::stringstream string_stream;
        string_stream << std::fixed << number;
        *this = string_stream.str();
        return *this;
    }
    inline friend bool operator > (BigFloat first_object, BigFloat second_object)
    {
        return first_object.Numerator * second_object.Denominator > second_object.Numerator * first_object.Denominator;
    }
    inline friend bool operator < (BigFloat first_object, BigFloat second_object)
    {
        return first_object.Numerator * second_object.Denominator < second_object.Numerator * first_object.Denominator;
    }
    inline friend bool operator == (BigFloat first_object, BigFloat second_object)
    {
        return first_object.Numerator * second_object.Denominator == second_object.Numerator * first_object.Denominator;
    }
    inline friend bool operator >= (BigFloat first_object, BigFloat second_object)
    {
        return first_object.Numerator * second_object.Denominator >= second_object.Numerator * first_object.Denominator;
    }
    inline friend bool operator <= (BigFloat first_object, BigFloat second_object)
    {
        return first_object.Numerator * second_object.Denominator <= second_object.Numerator * first_object.Denominator;
    }
    inline friend bool operator != (BigFloat first_object, BigFloat second_object)
    {
        return first_object.Numerator * second_object.Denominator != second_object.Numerator * first_object.Denominator;
    }
    template<typename T>
    inline friend bool operator > (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object > second_object;
    }
    template<typename T>
    inline friend bool operator < (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object < second_object;
    }
    template<typename T>
    inline friend bool operator == (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object == second_object;
    }
    template<typename T>
    inline friend bool operator >= (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object >= second_object;
    }
    template<typename T>
    inline friend bool operator <= (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object <= second_object;
    }
    template<typename T>
    inline friend bool operator != (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object != second_object;
    }
    template<typename T>
    inline friend bool operator > (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object > second_object;
    }
    template<typename T>
    inline friend bool operator < (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object < second_object;
    }
    template<typename T>
    inline friend bool operator == (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object == second_object;
    }
    template<typename T>
    inline friend bool operator >= (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object >= second_object;
    }
    template<typename T>
    inline friend bool operator <= (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object <= second_object;
    }
    template<typename T>
    inline friend bool operator != (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object != second_object;
    }
    inline friend bool operator > (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object > second_object;
    }
    inline friend bool operator < (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object < second_object;
    }
    inline friend bool operator == (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object == second_object;
    }
    inline friend bool operator >= (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object >= second_object;
    }
    inline friend bool operator <= (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object <= second_object;
    }
    inline friend bool operator != (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object != second_object;
    }
    inline friend bool operator > (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object > second_object;
    }
    inline friend bool operator < (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object < second_object;
    }
    inline friend bool operator == (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object == second_object;
    }
    inline friend bool operator >= (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object >= second_object;
    }
    inline friend bool operator <= (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object <= second_object;
    }
    inline friend bool operator != (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object != second_object;
    }
    inline friend BigFloat operator - (BigFloat object)
    {
        return 0 - object;
    }
    inline friend BigFloat operator + (BigFloat first_object, BigFloat second_object)
    {
        first_object.Numerator = first_object.Numerator * second_object.Denominator + second_object.Numerator * first_object.Denominator;
        first_object.Denominator *= second_object.Denominator;
        first_object.shrink_to_fit();
        return first_object;
    }
    inline friend BigFloat operator - (BigFloat first_object, BigFloat second_object)
    {
        first_object.Numerator = first_object.Numerator * second_object.Denominator - second_object.Numerator * first_object.Denominator;
        first_object.Denominator *= second_object.Denominator;
        first_object.shrink_to_fit();
        return first_object;
    }
    inline friend BigFloat operator * (BigFloat first_object, BigFloat second_object)
    {
        first_object.Numerator *= second_object.Numerator;
        first_object.Denominator *= second_object.Denominator;
        first_object.shrink_to_fit();
        return first_object;
    }
    inline friend BigFloat operator / (BigFloat first_object, BigFloat second_object)
    {
        first_object.Numerator *= second_object.Denominator;
        first_object.Denominator *= second_object.Numerator;
        first_object.shrink_to_fit();
        return first_object;
    }
    inline friend BigFloat operator % (BigFloat object, BigInt MOD)
    {
        object.Numerator *= pow(object.Denominator, phi(MOD) - 1);
        object.Numerator %= MOD;
        object.Denominator = 1;
        return object;
    }
    template<typename T>
    inline friend BigFloat operator + (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object + second_object;
    }
    template<typename T>
    inline friend BigFloat operator - (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object - second_object;
    }
    template<typename T>
    inline friend BigFloat operator * (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object * second_object;
    }
    template<typename T>
    inline friend BigFloat operator / (BigFloat first_object, T number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object / second_object;
    }
    inline friend BigFloat operator % (BigFloat object, int MOD)
    {
        object.Numerator *= pow(object.Denominator, phi(MOD) - 1);
        object.Numerator %= MOD;
        object.Denominator = 1;
        return object;
    }
    template<typename T>
    inline friend BigFloat operator + (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object + second_object;
    }
    template<typename T>
    inline friend BigFloat operator - (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object - second_object;
    }
    template<typename T>
    inline friend BigFloat operator * (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object * second_object;
    }
    template<typename T>
    inline friend BigFloat operator / (T number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object / second_object;
    }
    inline friend BigFloat operator + (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object + second_object;
    }
    inline friend BigFloat operator - (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object - second_object;
    }
    inline friend BigFloat operator * (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object * second_object;
    }
    inline friend BigFloat operator / (BigFloat first_object, BigInt number)
    {
        BigFloat second_object;
        second_object = number;
        return first_object / second_object;
    }
    inline friend BigFloat operator + (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object + second_object;
    }
    inline friend BigFloat operator - (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object - second_object;
    }
    inline friend BigFloat operator * (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object * second_object;
    }
    inline friend BigFloat operator / (BigInt number, BigFloat second_object)
    {
        BigFloat first_object;
        first_object = number;
        return first_object / second_object;
    }
    template<typename T>
    inline BigFloat& operator += (T number)
    {
        *this = *this + number;
        return *this;
    }
    template<typename T>
    inline BigFloat& operator -= (T number)
    {
        *this = *this - number;
        return *this;
    }
    template<typename T>
    inline BigFloat& operator *= (T number)
    {
        *this = *this * number;
        return *this;
    }
    template<typename T>
    inline BigFloat& operator /= (T number)
    {
        *this = *this / number;
        return *this;
    }
    template<typename T>
    inline BigFloat& operator %= (T number)
    {
        *this = *this % number;
        return *this;
    }
    inline BigFloat& operator += (BigInt number)
    {
        *this = *this + number;
        return *this;
    }
    inline BigFloat& operator -= (BigInt number)
    {
        *this = *this - number;
        return *this;
    }
    inline BigFloat& operator *= (BigInt number)
    {
        *this = *this * number;
        return *this;
    }
    inline BigFloat& operator /= (BigInt number)
    {
        *this = *this / number;
        return *this;
    }
    inline BigFloat& operator %= (BigInt number)
    {
        *this = *this % number;
        return *this;
    }
    inline BigFloat& operator ++ ()
    {
        Numerator += Denominator;
        return (*this);
    }
    inline BigFloat operator ++ (int32_t)
    {
        Numerator += Denominator;
        return (*this) - 1;
    }
    inline BigFloat& operator -- ()
    {
        Numerator -= Denominator;
        return (*this);
    }
    inline BigFloat operator -- (int32_t)
    {
        Numerator -= Denominator;
        return (*this) + 1;
    }
};
inline BigFloat abs(BigFloat number)
{
    BigInt Numerator = number.numerator();
    Numerator.is_negative = false;
    number.numerator(Numerator);
    BigInt Denominator = number.denominator();
    Denominator.is_negative = false;
    number.denominator(Denominator);
    return number;
}
BigFloat floor(BigFloat number, int Digits = 0)
{
    if (number.denominator() == 0)
    {
        return number;
    }
    number = number.str(Digits);
    return number;
}
BigFloat ceil(BigFloat number, int Digits = 0)
{
    if (number.denominator() == 0)
    {
        return number;
    }
    BigFloat number2;
    number2.numerator(1);
    std::string temp = "1";
    while (Digits--)
    {
        temp.push_back('0');
    }
    number2.denominator(temp);
    number += number2;
    number2.denominator(number.denominator());
    number -= number2;
    return number;
}
BigFloat round(BigFloat number, int Digits = 0)
{
    if (number.denominator() == 0)
    {
        return number;
    }
    std::string temp = number.str(Digits + 1);
    if (temp[temp.size() - 1] >= '5')
    {
        temp = '0' + temp;
        for (int i = temp.size() - 2; i >= 0; i--)
        {
            if (temp[i] == '.')
            {
                continue;
            }
            if (temp[i] != '9')
            {
                temp[i]++;
                break;
            }
            else
            {
                temp[i] = '0';
            }
        }
    }
    temp.pop_back();
    number = temp;
    return number;
}
BigFloat sqrt(BigInt number, int depth = 7)
{
    BigFloat temp = 0;
    BigFloat ans = 1;
    while (ans != temp)
    {
        temp = ans;
        ans = (5 * temp) / 4 + number / (4 * temp) - (temp * temp * temp) / (temp * temp + number);
        ans = floor(ans, depth);
    }
    return ans;
}
BigFloat sqrt(BigFloat number, int depth = 7)
{
    BigFloat temp = 0;
    BigFloat ans = 1;
    while (ans != temp)
    {
        temp = ans;
        ans = (5 * temp) / 4 + number / (4 * temp) - (temp * temp * temp) / (temp * temp + number);
        ans = floor(ans, depth);
    }
    return ans;
}
BigFloat cbrt(BigInt number, int depth = 7)
{
    BigFloat temp = 0;
    BigFloat ans = 1;
    while (ans != temp)
    {
        temp = ans;
        ans = temp - (temp * temp * temp - number) / (3 * temp * temp);
        ans = floor(ans, depth);
    }
    return ans;
}
BigFloat cbrt(BigFloat number, int depth = 7)
{
    BigFloat temp = 0;
    BigFloat ans = 1;
    while (ans != temp)
    {
        temp = ans;
        ans = temp - (temp * temp * temp - number) / (3 * temp * temp);
        ans = floor(ans, depth);
    }
    return ans;
}
int main()
{
    return 0;
}