#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#ifdef iq
mt19937 rnd(228);
#else
mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());
#endif
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 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>
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 = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
template <typename T>
class NTT {
public:
using Type = typename decay<decltype(T::value)>::type;
static Type md;
static Modular<T> root;
static int base;
static int max_base;
static vector<Modular<T>> roots;
static vector<int> rev;
static void clear() {
root = 0;
base = 0;
max_base = 0;
roots.clear();
rev.clear();
}
static void init() {
md = T::value;
assert(md >= 3 && md % 2 == 1);
auto tmp = md - 1;
max_base = 0;
while (tmp % 2 == 0) {
tmp /= 2;
max_base++;
}
root = 2;
while (power(root, (md - 1) >> 1) == 1) {
root++;
}
assert(power(root, md - 1) == 1);
root = power(root, (md - 1) >> max_base);
base = 1;
rev = {0, 1};
roots = {0, 1};
}
static void ensure_base(int nbase) {
if (md != T::value) {
clear();
}
if (roots.empty()) {
init();
}
if (nbase <= base) {
return;
}
assert(nbase <= max_base);
rev.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
roots.resize(1 << nbase);
while (base < nbase) {
Modular<T> z = power(root, 1 << (max_base - 1 - base));
for (int i = 1 << (base - 1); i < (1 << base); i++) {
roots[i << 1] = roots[i];
roots[(i << 1) + 1] = roots[i] * z;
}
base++;
}
}
static void fft(vector<Modular<T>> &a) {
int n = (int) a.size();
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
Modular<T> x = a[i + j];
Modular<T> y = a[i + j + k] * roots[j + k];
a[i + j] = x + y;
a[i + j + k] = x - y;
}
}
}
}
static vector<Modular<T>> multiply(vector<Modular<T>> a, vector<Modular<T>> b) {
if (a.empty() || b.empty()) {
return {};
}
int eq = (a == b);
int need = (int) a.size() + (int) b.size() - 1;
int nbase = 0;
while ((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz);
b.resize(sz);
fft(a);
if (eq) b = a; else fft(b);
Modular<T> inv_sz = 1 / static_cast<Modular<T>>(sz);
for (int i = 0; i < sz; i++) {
a[i] *= b[i] * inv_sz;
}
reverse(a.begin() + 1, a.end());
fft(a);
a.resize(need);
return a;
}
};
template <typename T> typename NTT<T>::Type NTT<T>::md;
template <typename T> Modular<T> NTT<T>::root;
template <typename T> int NTT<T>::base;
template <typename T> int NTT<T>::max_base;
template <typename T> vector<Modular<T>> NTT<T>::roots;
template <typename T> vector<int> NTT<T>::rev;
template <typename T>
vector<Modular<T>> inverse(const vector<Modular<T>>& a) {
assert(!a.empty());
int n = (int) a.size();
vector<Modular<T>> b = {1 / a[0]};
while ((int) b.size() < n) {
vector<Modular<T>> x(a.begin(), a.begin() + min(a.size(), b.size() << 1));
x.resize(b.size() << 1);
b.resize(b.size() << 1);
vector<Modular<T>> c = b;
NTT<T>::fft(c);
NTT<T>::fft(x);
Modular<T> inv = 1 / static_cast<Modular<T>>((int) x.size());
for (int i = 0; i < (int) x.size(); i++) {
x[i] *= c[i] * inv;
}
reverse(x.begin() + 1, x.end());
NTT<T>::fft(x);
rotate(x.begin(), x.begin() + (x.size() >> 1), x.end());
fill(x.begin() + (x.size() >> 1), x.end(), 0);
NTT<T>::fft(x);
for (int i = 0; i < (int) x.size(); i++) {
x[i] *= c[i] * inv;
}
reverse(x.begin() + 1, x.end());
NTT<T>::fft(x);
for (int i = 0; i < ((int) x.size() >> 1); i++) {
b[i + ((int) x.size() >> 1)] = -x[i];
}
}
b.resize(n);
return b;
}
template <typename T>
vector<Modular<T>> inverse_old(vector<Modular<T>> a) {
assert(!a.empty());
int n = (int) a.size();
if (n == 1) {
return {1 / a[0]};
}
int m = (n + 1) >> 1;
vector<Modular<T>> b = inverse(vector<Modular<T>>(a.begin(), a.begin() + m));
int need = n << 1;
int nbase = 0;
while ((1 << nbase) < need) {
++nbase;
}
NTT<T>::ensure_base(nbase);
int size = 1 << nbase;
a.resize(size);
b.resize(size);
NTT<T>::fft(a);
NTT<T>::fft(b);
Modular<T> inv = 1 / static_cast<Modular<T>>(size);
for (int i = 0; i < size; ++i) {
a[i] = (2 - a[i] * b[i]) * b[i] * inv;
}
reverse(a.begin() + 1, a.end());
NTT<T>::fft(a);
a.resize(n);
return a;
}
template <typename T>
vector<Modular<T>> operator*(const vector<Modular<T>>& a, const vector<Modular<T>>& b) {
if (a.empty() || b.empty()) {
return {};
}
if (min(a.size(), b.size()) < 150) {
vector<Modular<T>> c(a.size() + b.size() - 1, 0);
for (int i = 0; i < (int) a.size(); i++) {
for (int j = 0; j < (int) b.size(); j++) {
c[i + j] += a[i] * b[j];
}
}
return c;
}
return NTT<T>::multiply(a, b);
}
template <typename T>
vector<Modular<T>>& operator*=(vector<Modular<T>>& a, const vector<Modular<T>>& b) {
return a = a * b;
}
const int N = 1e6 + 228;
Mint fact[N], rfact[N];
int main() {
#ifdef iq
freopen("a.in", "r", stdin);
#endif
ios::sync_with_stdio(0);
cin.tie(0);
fact[0] = 1;
for (int i = 1; i < N; i++) {
fact[i] = fact[i - 1] * i;
}
rfact[N - 1] = 1 / fact[N - 1];
for (int i = N - 2; i >= 0; i--) {
rfact[i] = (i + 1) * rfact[i + 1];
}
int t;
cin >> t;
while (t--) {
int n, p, r;
cin >> n >> p >> r;
//x(x-1)...(x-n+1)
function<vector<Mint>(int)> f = [&] (int n) {
if (n == 0) {
vector <Mint> t;
t.push_back(1);
return t;
} else if (n % 2) {
auto ok = f(n - 1);
vector <Mint> p;
p.push_back(-n + 1);
p.push_back(1);
return ok * p;
} else {
auto ok = f(n / 2);
int c = -(n / 2);
//((x+c)^i) -> sum(x^j*c^(i-j)*i!/j!/(i-j)!)
auto a = ok;
for (int i = 0; i < (int) a.size(); i++) {
a[i] = a[i] * fact[i];
}
vector <Mint> t(ok.size());
t[0] = 1;
for (int i = 1; i < (int) ok.size(); i++) {
t[i] = t[i - 1] * c;
}
for (int i = 0; i < (int) t.size(); i++) {
t[i] = t[i] * rfact[i];
}
reverse(t.begin(), t.end());
auto mda = a * t;
int sign = (int) t.size() - 1;
vector <Mint> b(mda.size() - sign);
for (int i = sign; i < (int) mda.size(); i++) {
b[i - sign] += mda[i];
}
for (int i = 0; i < (int) b.size(); i++) {
b[i] = b[i] * rfact[i];
}
return ok * b;
}
};
auto ans = f(r);
n++;
Mint me = 1;
Mint ret = 0;
for (int i = 0; i < (int) ans.size(); i++) {
if (me == 1) {
ret += n * ans[i];
} else {
ret += (power(me, n) - 1) / (me - 1) * ans[i];
}
/*
Ot cur = power(me, n) - 1;
// += ans[i] * (me^n - 1)/(me-1)
//me^0 + me^1 + ... +me^(n-1)
*/
me *= p;
}
cout << ret * rfact[r] << endl;
}
}