// #pragma comment(linker, "/stack:200000000") // #pragma GCC optimize("Ofast") // #pragma GCC optimize ("unroll-loops") // #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") // codeforces //#pragma GCC target("avx,avx2,fma") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,tune=native") // yandex #include "bits/stdc++.h" using namespace std; #ifndef LOCAL #define endl '\n' #endif #define fr(i, a, b) for(int i = a; i <= b; i++) #define rf(i, a, b) for(int i = a; i >= b; i--) #define pf push_front #define pb push_back #define eb emplace_back #define fi first #define se second #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() #define lb lower_bound #define ub upper_bound typedef long long ll; typedef long double f80; typedef pair<int,int> pii; typedef pair<ll,ll> pll; int pct(int x) { return __builtin_popcount(x); } int pct(ll x) { return __builtin_popcountll(x); } int bt(int x) { return 31 - __builtin_clz(x); } // floor(log2(x)) int bt(ll x) { return 63 - __builtin_clzll(x); } // floor(log2(x)) int cdiv(int a, int b) { return a / b + !(a < 0 || a % b == 0); } ll cdiv(ll a, ll b) { return a / b + !(a < 0 || a % b == 0); } int nxt_C(int x) { int c = x & -x, r = x + c; return (((r ^ x) >> 2) / c) | r; } ll nxt_C(ll x) { ll c = x & -x, r = x + c; return (((r ^ x) >> 2) / c) | r; } vector<int> get_bits(int mask) { vector<int> bb; while(mask) { int b = bt(mask); bb.pb(b); mask ^= (1 << b); } reverse(all(bb)); return bb; } int get_mask(vector<int> v) { int mask = 0; for(int x : v) { mask ^= (1 << x); } return mask; } template<typename T> void uniq(vector<T> &v) { sort(all(v)); v.resize(unique(all(v)) - v.begin()); } mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()); ll rand(ll l, ll r){ uniform_int_distribution<ll> uid(l, r); return uid(rng); } void sc() {} template <typename Head, typename... Tail> void sc(Head &H, Tail &... T) { cin >> H; sc(T...); } #ifdef LOCAL #define debug(...) cerr << "[L:" << __LINE__ << "][" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif // #ifndef LOCAL // string to_string(__int128 x) { // string s = ""; // bool neg = 0; // if(x < 0) { s += "-"; neg = 1; x = -x; } // if(!x) s += '0'; // while(x) { // int rem = x % 10; // s += to_string(rem); // x /= 10; // } // reverse(s.begin() + neg, s.end()); // return s; // } // #endif const int mod = 1e9 + 7; // 998244353; int pwr(int a,ll b) { int ans = 1; while(b) { if(b & 1) ans = (ans * 1LL * a) % mod; a = (a * 1LL * a) % mod; b >>= 1; } return ans; } /* Lookout for overflows!! Check array sizes!! Clear before test cases!! Use the correct modulo!! Check for corner cases!! Are you forgetting something?! Read problem statement carefully!!! */ template <typename T> T inverse(T a, T m) { T u = 0, v = 1; while (a != 0) { T t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return u; } template <typename T> class Modular { public: using Type = typename decay<decltype(T::value)>::type; constexpr Modular() : value() {} template <typename U> Modular(const U& x) { value = normalize(x); } template <typename U> static Type normalize(const U& x) { Type v; if (-mod() <= x && x < mod()) v = static_cast<Type>(x); else v = static_cast<Type>(x % mod()); if (v < 0) v += mod(); return v; } const Type& operator()() const { return value; } template <typename U> explicit operator U() const { return static_cast<U>(value); } constexpr static Type mod() { return T::value; } Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; } Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; } template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); } template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); } Modular& operator++() { return *this += 1; } Modular& operator--() { return *this -= 1; } Modular operator++(int) { Modular result(*this); *this += 1; return result; } Modular operator--(int) { Modular result(*this); *this -= 1; return result; } Modular operator-() const { return Modular(-value); } template <typename U = T> typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) { #ifdef _WIN32 uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value); uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m; asm( "divl %4; \n\t" : "=a" (d), "=d" (m) : "d" (xh), "a" (xl), "r" (mod()) ); value = m; #else value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value)); #endif return *this; } template <typename U = T> typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) { int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod()); value = normalize(value * rhs.value - q * mod()); return *this; } template <typename U = T> typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) { value = normalize(value * rhs.value); return *this; } Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); } template <typename U> friend const Modular<U>& abs(const Modular<U>& v) { return v; } template <typename U> friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs); template <typename U> friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs); template <typename U> friend std::istream& operator>>(std::istream& stream, Modular<U>& number); private: Type value; }; template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; } template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); } template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; } template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); } template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); } template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); } template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; } template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; } template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; } template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; } template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; } template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; } template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; } template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; } template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; } template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; } template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; } template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; } template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; } template<typename T, typename U> Modular<T> power(const Modular<T>& a, const U& b) { assert(b >= 0); Modular<T> x = a, res = 1; U p = b; while (p > 0) { if (p & 1) res *= x; x *= x; p >>= 1; } return res; } template <typename T> bool IsZero(const Modular<T>& number) { return number() == 0; } template <typename T> string to_string(const Modular<T>& number) { return to_string(number()); } template <typename T> std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) { return stream << number(); } template <typename T> std::istream& operator>>(std::istream& stream, Modular<T>& number) { typename common_type<typename Modular<T>::Type, int64_t>::type x; stream >> x; number.value = Modular<T>::normalize(x); return stream; } /* using ModType = int; struct VarMod { static ModType value; }; ModType VarMod::value; ModType& md = VarMod::value; using Mint = Modular<VarMod>; */ constexpr int md = 1e9 + 7; using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>; Mint pwr(Mint a, ll k) { Mint ans = 1; while(k) { if(k & 1) ans = ans * a; a = a * a; k >>= 1; } return ans; } const int N = 205; Mint dp[2][N][N][N]; Mint ans[N][N]; void solve() { dp[1][1][1][1] = 1; dp[1][2][1][1] = -1; fr(i, 1, N - 2) { int i1 = i & 1, i2 = i1 ^ 1; fr(j, 1, i + 1) { fr(k, 1, i + 1) { fr(l, k, i + 1) { dp[i2][j][k][l] = 0; } } } fr(k, 1, i) { fr(l, k, i) { fr(j, 1, i) { dp[i1][j][k][l] += dp[i1][j - 1][k][l]; Mint val = dp[i1][j][k][l]; ans[i][l] += val; dp[i2][j + 1][k + 1][max(k + 1, l)] += val; dp[i2][1][1][l] += val; dp[i2][j + 1][1][l] -= val; } } } } int t; sc(t); while(t--) { int n, k; sc(n, k); cout << ans[n][k] << endl; } } int main() { freopen("permutations.in", "r", stdin); ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0); int t = 1; // cin >> t; for(int tt = 1; tt <= t; tt++) { solve(); } return 0; }
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