// https://loj.ac/p/138 #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } //////////////////////////////////////////////////////////////////////////////// template struct ModInt { static constexpr unsigned M = M_; unsigned x; constexpr ModInt() : x(0U) {} constexpr ModInt(unsigned x_) : x(x_ % M) {} constexpr ModInt(unsigned long long x_) : x(x_ % M) {} constexpr ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} constexpr ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { x = (static_cast(x) * a.x) % M; return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; //////////////////////////////////////////////////////////////////////////////// constexpr unsigned MO = 998244353; using Mint = ModInt; constexpr int LIM_INV = 110; Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV]; void prepare() { inv[1] = 1; for (int i = 2; i < LIM_INV; ++i) { inv[i] = -((Mint::M / i) * inv[Mint::M % i]); } fac[0] = invFac[0] = 1; for (int i = 1; i < LIM_INV; ++i) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(Int n, Int k) { if (n < 0) { if (k >= 0) { return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k); } else if (n - k >= 0) { return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k); } else { return 0; } } else { if (0 <= k && k <= n) { assert(n < LIM_INV); return fac[n] * invFac[k] * invFac[n - k]; } else { return 0; } } } template T pathUnder(S m, S a, S b, S n, T e, T x, T y) { assert(m >= 1); assert(a >= 0); assert(b >= 0); assert(n >= 0); S c = (a * n + b) / m; T pre = e, suf = e; for (; ; ) { const S p = a / m; a %= m; x = x * y.pow(p); const S q = b / m; b %= m; pre = pre * y.pow(q); c -= (p * n + q); if (c == 0) return pre * x.pow(n) * suf; const S d = (m * c - b - 1) / a + 1; suf = y * x.pow(n - d) * suf; b = m - b - 1 + a; swap(m, a); n = c - 1; c = d; swap(x, y); } } constexpr int MAX = 11; Mint bn[MAX][MAX]; int K, L; struct Data { Mint dx, dy; Mint sum[MAX][MAX]; Data() : dx(0), dy(0), sum{} {} friend Data operator*(const Data &a, const Data &b) { Data c; c.dx = a.dx + b.dx; c.dy = a.dy + b.dy; for (int k = 0; k <= K; ++k) for (int l = 0; l <= L; ++l) { c.sum[k][l] += a.sum[k][l]; } Mint tmp[MAX][MAX]; for (int k = 0; k <= K; ++k) for (int l = 0; l <= L; ++l) { Mint pw = 1; for (int kk = 0; kk <= k; ++kk) { tmp[k][l] += bn[k][kk] * pw * b.sum[k - kk][l]; pw *= a.dx; } } for (int k = 0; k <= K; ++k) for (int l = 0; l <= L; ++l) { Mint pw = 1; for (int ll = 0; ll <= l; ++ll) { c.sum[k][l] += bn[l][ll] * pw * tmp[k][l - ll]; pw *= a.dy; } } return c; } Data pow(Int e) const { Data a = *this, b; for (; ; a = a * a) { if (e & 1) b = b * a; if (!(e >>= 1)) return b; } } }; // floor(a / b) template T divFloor(T a, T b) { return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0); } // ceil(a / b) template T divCeil(T a, T b) { return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0); } int main() { prepare(); for (int n = 0; n < MAX; ++n) { bn[n][0] = bn[n][n] = 1; for (int k = 1; k < n; ++k) { bn[n][k] = bn[n - 1][k - 1] + bn[n - 1][k]; } } for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) { Int N, A, B, C; // scanf("%lld%lld%lld%lld%d%d", &N, &A, &B, &C, &K, &L); scanf("%d%d%lld%lld%lld%lld", &K, &L, &N, &C, &A, &B); bool neg = false; if (A < 0) { neg = true; B += A * N; A = -A; } Int BQ = B / C; Int BR = B % C; if (BR < 0) { BQ -= 1; BR += C; } // cerr<(C, A, BR, N + 1, Data(), X, Y); // printf("%u\n", res.sum[K][L].x); Mint ans = 0; if (neg) { // (N-i)^K (BQ+j)^L for (int k = 0; k <= K; ++k) for (int l = 0; l <= L; ++l) { ans += bn[K][k] * bn[L][l] * Mint(N).pow(K - k) * Mint(BQ).pow(L - l) * (k&1?-1:+1) * res.sum[k][l]; } } else { // i^K (BQ+j)^L for (int l = 0; l <= L; ++l) { ans += bn[L][l] * Mint(BQ).pow(l) * res.sum[K][L - l]; } } printf("%u\n", ans.x); } #ifndef LOCAL break; #endif } return 0; }