結果

問題 No.2996 Floor Sum
コンテスト
ユーザー ecottea
提出日時 2025-06-21 03:09:19
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 320 ms / 5,000 ms
コード長 27,987 bytes
コンパイル時間 10,090 ms
コンパイル使用メモリ 411,300 KB
実行使用メモリ 7,844 KB
最終ジャッジ日時 2025-06-21 03:09:33
合計ジャッジ時間 12,241 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 12
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ソースコード

diff # 

// QCFium 法
//#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")


#ifndef HIDDEN_IN_VS // 折りたたみ用

// 警告の抑制
#define _CRT_SECURE_NO_WARNINGS

// ライブラリの読み込み
#include <bits/stdc++.h>
using namespace std;

// 型名の短縮
using ll = long long; using ull = unsigned long long; // -2^63 ～ 2^63 = 9e18（int は -2^31 ～ 2^31 = 2e9）
using pii = pair<int, int>;	using pll = pair<ll, ll>;	using pil = pair<int, ll>;	using pli = pair<ll, int>;
using vi = vector<int>;		using vvi = vector<vi>;		using vvvi = vector<vvi>;	using vvvvi = vector<vvvi>;
using vl = vector<ll>;		using vvl = vector<vl>;		using vvvl = vector<vvl>;	using vvvvl = vector<vvvl>;
using vb = vector<bool>;	using vvb = vector<vb>;		using vvvb = vector<vvb>;
using vc = vector<char>;	using vvc = vector<vc>;		using vvvc = vector<vvc>;
using vd = vector<double>;	using vvd = vector<vd>;		using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;

// 定数の定義
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4 近傍（下，右，上，左）
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;

// 入出力高速化
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;

// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順
#define repe(v, a) for(const auto& v : (a)) // a の全要素（変更不可能）
#define repea(v, a) for(auto& v : (a)) // a の全要素（変更可能）
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索（昇順）
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素（昇順）
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て（昇順）
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
#define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定

// 汎用関数の定義
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新（更新されたら true を返す）
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新（更新されたら true を返す）
template <class T> inline T getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // 非負mod

// 演算子オーバーロード
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }

#endif // 折りたたみ用


#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;

#ifdef _MSC_VER
#include "localACL.hpp"
#endif

using mint = modint998244353;
//using mint = static_modint<1000000007>;
//using mint = modint; // mint::set_mod(m);

namespace atcoder {
	inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
	inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif


#ifdef _MSC_VER // 手元環境（Visual Studio）
#include "local.hpp"
#else // 提出用（gcc）
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(...)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE の代わりに MLE を出す
#endif


//【直線に沿った格子路上の積】O(log(n + m))
/*
* (0, 0) から (n, (an+b)//m) までの直線 y=(ax+b)/m 以下の上方向優先の最短格子路について，
* 右に進むときは f，上に進むときは g を順に掛け合わせたモノイド (S, op, e) の元を返す．
*
* 制約：n≧0, m≧1, a≧0, b≧0
*/
template <class T, class S, S(*op)(S, S), S(*e)()>
S multiple_along_line(T n, T m, T a, T b, S f, S g) {
	// 参考 : https://github.com/hos-lyric/libra/blob/master/number/gojo.cpp
	// verify : https://judge.yosupo.jp/problem/sum_of_floor_of_linear

	Assert(n >= 0); Assert(m >= 1); Assert(a >= 0); Assert(b >= 0);

	// x^n を返す
	auto pow = [](const S& x, T n) {
		S res(e()), pow2 = x;
		while (n > 0) {
			if (n & 1) res = op(res, pow2);
			pow2 = op(pow2, pow2);
			n /= 2;
		}
		return res;
	};

	S resL = e(), resR = e(); bool rev = false;

	while (true) {
		// 傾きを 1 未満，切片を 1 未満にする．
		if (rev) {
			resR = op(pow(g, b / m), resR);
			f = op(pow(g, a / m), f);
		}
		else {
			resL = op(resL, pow(g, b / m));
			f = op(f, pow(g, a / m));
		}

		a %= m;
		b %= m;
		if (a == 0 || n == 0) break;

		// 左側の中途半端に余っている部分を切り取る．
		T l = (m - b + a - 1) / a;
		if (l > n) {
			if (rev) {
				resR = op(pow(f, n), resR);
			}
			else {
				resL = op(resL, pow(f, n));
			}
			n = 0;
			break;
		}

		if (rev) {
			resR = op(op(g, pow(f, l)), resR);
		}
		else {
			resL = op(resL, op(pow(f, l), g));
		}

		b = a * l + b - m;
		n -= l;
		if (n == 0) break;

		// 軸を取り直して傾きを 1 より大きくする．
		T nn = (a * n + b) / m;
		T nm = a;
		T na = m;
		T nb = a * n + b - m * nn;

		n = nn; m = nm; a = na; b = nb; swap(f, g);
		rev = !rev;
	}

	return op(resL, op(pow(f, n), resR));
}


//【階乗など（法が大きな素数）】
/*
* Factorial_mint(int N) : O(n)
*	N まで計算可能として初期化する．
*
* mint fact(int n) : O(1)
*	n! を返す．
*
* mint fact_inv(int n) : O(1)
*	1/n! を返す（n が負なら 0 を返す）
*
* mint inv(int n) : O(1)
*	1/n を返す．
*
* mint perm(int n, int r) : O(1)
*	順列の数 nPr を返す．
*
* mint bin(int n, int r) : O(1)
*	二項係数 nCr を返す．
*
* mint bin_inv(int n, int r) : O(1)
*	二項係数の逆数 1/nCr を返す．
*
* mint mul(vi rs) : O(|rs|)
*	多項係数 nC[rs] を返す．（n = Σrs）
*
* mint hom(int n, int r) : O(1)
*	重複組合せの数 nHr = n+r-1Cr を返す（0H0 = 1 とする）
*
* mint neg_bin(int n, int r) : O(1)
*	負の二項係数 nCr = (-1)^r -n+r-1Cr を返す（n ≦ 0, r ≧ 0）
*/
class Factorial_mint {
	int n_max;

	// 階乗と階乗の逆数の値を保持するテーブル
	vm fac, fac_inv;

public:
	// n! までの階乗とその逆数を前計算しておく．O(n)
	Factorial_mint(int n) : n_max(n), fac(n + 1), fac_inv(n + 1) {
		// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b

		fac[0] = 1;
		repi(i, 1, n) fac[i] = fac[i - 1] * i;

		fac_inv[n] = fac[n].inv();
		repir(i, n - 1, 0) fac_inv[i] = fac_inv[i + 1] * (i + 1);
	}
	Factorial_mint() : n_max(0) {} // ダミー

	// n! を返す．
	mint fact(int n) const {
		// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b

		Assert(0 <= n && n <= n_max);
		return fac[n];
	}

	// 1/n! を返す（n が負なら 0 を返す）
	mint fact_inv(int n) const {
		// verify : https://atcoder.jp/contests/abc289/tasks/abc289_h

		Assert(n <= n_max);
		if (n < 0) return 0;
		return fac_inv[n];
	}

	// 1/n を返す．
	mint inv(int n) const {
		// verify : https://atcoder.jp/contests/exawizards2019/tasks/exawizards2019_d

		Assert(n > 0);
		Assert(n <= n_max);
		return fac[n - 1] * fac_inv[n];
	}

	// 順列の数 nPr を返す．
	mint perm(int n, int r) const {
		// verify : https://atcoder.jp/contests/abc172/tasks/abc172_e

		Assert(n <= n_max);

		if (r < 0 || n - r < 0) return 0;
		return fac[n] * fac_inv[n - r];
	}

	// 二項係数 nCr を返す．
	mint bin(int n, int r) const {
		// verify : https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod

		Assert(n <= n_max);
		if (r < 0 || n - r < 0) return 0;
		return fac[n] * fac_inv[r] * fac_inv[n - r];
	}

	// 二項係数の逆数 1/nCr を返す．
	mint bin_inv(int n, int r) const {
		// verify : https://www.codechef.com/problems/RANDCOLORING

		Assert(n <= n_max);
		Assert(r >= 0);
		Assert(n - r >= 0);
		return fac_inv[n] * fac[r] * fac[n - r];
	}

	// 多項係数 nC[rs] を返す．
	mint mul(const vi& rs) const {
		// verify : https://yukicoder.me/problems/no/2141

		if (*min_element(all(rs)) < 0) return 0;
		int n = accumulate(all(rs), 0);
		Assert(n <= n_max);

		mint res = fac[n];
		repe(r, rs) res *= fac_inv[r];

		return res;
	}

	// 重複組合せの数 nHr = n+r-1Cr を返す（0H0 = 1 とする）
	mint hom(int n, int r) {
		// verify : https://mojacoder.app/users/riantkb/problems/toj_ex_2

		if (n == 0) return (int)(r == 0);
		Assert(n + r - 1 <= n_max);
		if (r < 0 || n - 1 < 0) return 0;
		return fac[n + r - 1] * fac_inv[r] * fac_inv[n - 1];
	}

	// 負の二項係数 nCr を返す（n ≦ 0, r ≧ 0）
	mint neg_bin(int n, int r) {
		// verify : https://atcoder.jp/contests/abc345/tasks/abc345_g

		if (n == 0) return (int)(r == 0);
		Assert(-n + r - 1 <= n_max);
		if (r < 0 || -n - 1 < 0) return 0;
		return (r & 1 ? -1 : 1) * fac[-n + r - 1] * fac_inv[r] * fac_inv[-n - 1];
	}
};
Factorial_mint fm(123);


//【一次式の累乗切り捨て和】O((P Q)^2 log(n + m))
/*
* Σi∈[0..n) i^P floor((a i + b) / m)^Q を返す．
* 
* 利用：【直線に沿った格子路上の積（モノイド）】
*/
int exapfs, eyapfs;
template <class T>
struct Sapfs {
	vector<T> v = vector<T>((exapfs + 1) * (eyapfs + 1));
	T f = 0, g = 0;

#ifdef _MSC_VER
	friend ostream& operator<<(ostream& os, const Sapfs& x) {
		os << "(" << x.v << "," << x.f << "," << x.g << ")";
		return os;
	}
#endif
};
template <class T> Sapfs<T> opapfs(Sapfs<T> b, Sapfs<T> a) {
	vector<vector<T>> bin_f(exapfs + 1, vector<T>(exapfs + 1));
	bin_f[0][0] = 1;
	repi(i, 1, exapfs) repi(j, 0, i) {
		if (j > 0) bin_f[i][j] += bin_f[i - 1][j - 1];
		if (j < i) bin_f[i][j] += bin_f[i - 1][j] * b.f;
	}

	vector<vector<T>> bin_g(eyapfs + 1, vector<T>(eyapfs + 1));
	bin_g[0][0] = 1;
	repi(i, 1, eyapfs) repi(j, 0, i) {
		if (j > 0) bin_g[i][j] += bin_g[i - 1][j - 1];
		if (j < i) bin_g[i][j] += bin_g[i - 1][j] * b.g;
	}

	repi(ix, 0, exapfs) repi(jx, 0, ix) {
		repi(iy, 0, eyapfs) repi(jy, 0, iy) {
			b.v[jx * (eyapfs + 1) + jy] += a.v[ix * (eyapfs + 1) + iy] * bin_f[ix][jx] * bin_g[iy][jy];
		}
	}

	b.f += a.f;
	b.g += a.g;

	return b;
}
template <class T> Sapfs<T> eapfs() {
	Sapfs<T> a;
	return a;
}
template <class T, class S>
S arithmetic_powered_floor_sum(T n, T m, T a, T b, int P, int Q) {
	// 参考 : https://qiita.com/sounansya/items/51b39e0d7bf5cc194081
	
	//【方法】
	// i^p floor((ai+b)/m)^q も一緒に計算していくことで行列積とみなせる．
	// クロネッカー積分解を考えることで計算量を落とせる．

	if (n <= 0) return S(0);
	
	Assert(m != 0);
	
	if (m < 0) {
		m = -m;
		a = -a;
		b = -b;
	}

	exapfs = P;
	eyapfs = Q;

	int L = max(P, Q);
	vector<vector<S>> bin(L + 1, vector<S>(L + 1));
	bin[0][0] = S(1);
	repi(i, 1, L) repi(j, 0, i) {
		if (j > 0) bin[i][j] += bin[i - 1][j - 1];
		if (j < i) bin[i][j] += bin[i - 1][j];
	}

	Sapfs<S> f;
	repi(i, 0, P) f.v[i * (Q + 1) + Q] = bin[P][i];
	f.f = S(1);

	Sapfs<S> g;
	repi(i, 1, Q) g.v[(P + 1) * (Q + 1) - 1 - i] = bin[Q][i];
	g.g = S(1);

	// a < 0 のときは Σi∈[0..n) i^P (-floor((a i + b) / m))^Q を求め，後で (-1)^Q 倍する．
	if (a < 0) b = m - T(1) - b;
	
	T br = smod(b, m);
	T bq = (b - br) / m;
	dump(br, bq);

	// (0, b/m) → (n-1, (a(n-1)+b)/m) の移動に対応する行列積を計算する．
	auto h = multiple_along_line<ll, Sapfs<S>, opapfs<S>, eapfs<S>>(n - 1, m, abs(a), br, f, g);
	dump(h);

	// (0, 0) → (0, b/m) の移動に対応する行列を右から掛ける．
	S res(0); S bq_pow(1);
	repi(i, 0, Q) {
		res += h.v[i] * bq_pow;
		if (i < Q) bq_pow *= bq;
	}
	if (P == 0) res += bq_pow;

	if ((a < 0) && (Q & 1)) res *= S(-1);

	return res;
}


//【切り捨て除算】O(1)
/*
* a, b の正負によらず，数学的な floor(a / b) を返す．
*/
template <class T>
T floor_div(T a, T b) {
	// verify : https://atcoder.jp/contests/abc315/tasks/abc315_g

	Assert(b != 0);

	// 分母が負の場合は，分子と分母に -1 を掛けて分母を正にする．
	if (b < 0) { a *= -1; b *= -1; };

	// 分子が非負の場合は，a / b で切り捨てになる．
	if (a >= 0) return a / b;
	// 分子が負の場合は，左右反転して切り上げ商を計算し，再度左右反転する．
	else return -((-a + b - 1) / b);
}


mint naive(ll n, ll m, ll a, ll b, int ex, int ey) {
	mint res = 0;

	rep(x, n) {
		ll y = floor_div(a * x + b, m);

		res += mint(x).pow(ex) * mint(y).pow(ey);
	}

	return res;
}


// 自動生成
namespace aaa {
	using S = tuple<mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint>;
	S op(S b, S a) {
		auto [a6, a8, a12, a15, a16, a21, a36, a38, a40, a42, a55, a64, a76, a88, a91, a96, a113, \
			a128, a192, a200, a262, a264, a302, a320, a433, a524, a576, a604, a704, a881, \
			a1394, a1600, a2024, a3413] = a;
		auto [b6, b8, b12, b15, b16, b21, b36, b38, b40, b42, b55, b64, b76, b88, b91, b96, b113, \
			b128, b192, b200, b262, b264, b302, b320, b433, b524, b576, b604, b704, b881, \
			b1394, b1600, b2024, b3413] = b;
		mint c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
			c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
			c1394, c1600, c2024, c3413;
		c6 = a6 + b6; c8 = a8 + b8; c12 = a12 + b12; c15 = a15 + a6 * b6 + b15; c16 = a16 + \
			b16; c21 = a21 + a6 * b6 + b21; c36 = a36 + a12 * b6 + b36; c38 = a38 + a6 * b8 + \
			b38; c40 = a40 + a8 * b6 + a6 * b8 + b40; c42 = a42 + a6 * b12 + b42; c55 = a55 + \
			a36 * b6 + a12 * b15 + b55; c64 = a64 + a16 * b8 + b64; c76 = a76 + a6 * b16 + \
			b76; c88 = a88 + a16 * b6 + a12 * b8 + b88; c91 = a91 + a42 * b6 + a6 * b36 + \
			b91; c96 = a96 + a16 * b6 + a6 * b16 + b96; c113 = a113 + a38 * b6 + a21 * b8 + \
			a6 * b40 + b113; c128 = a128 + a16 * b16 + b128; c192 = a192 + a16 * b12 + \
			a12 * b16 + b192; c200 = a200 + a88 * b6 + a36 * b8 + a16 * b15 + a12 * b40 + \
			b200; c262 = a262 + a76 * b8 + a6 * b64 + b262; c264 = a264 + a76 * b6 + a42 * b8 + \
			a6 * b88 + b264; c302 = a302 + a76 * b6 + a21 * b16 + a6 * b96 + b302; c320 = a320 \
			+ a64 * b6 + a96 * b8 + a16 * b40 + a6 * b64 + b320; c433 = a433 + a264 * b6 + \
			a91 * b8 + a76 * b15 + a42 * b40 + a6 * b200 + b433; c524 = a524 + a76 * b16 + \
			a6 * b128 + b524; c576 = a576 + a192 * b6 + a36 * b16 + a16 * b36 + a12 * b96 + \
			b576; c604 = a604 + a76 * b12 + a42 * b16 + a6 * b192 + b604; c704 = a704 + \
			a128 * b6 + a192 * b8 + a12 * b64 + a16 * b88 + b704; c881 = a881 + a262 * b6 + \
			a302 * b8 + a76 * b40 + a21 * b64 + a6 * b320 + b881; c1394 = a1394 + a604 * b6 + \
			a91 * b16 + a76 * b36 + a42 * b96 + a6 * b576 + b1394; c1600 = a1600 + a704 * b6 + \
			a576 * b8 + a128 * b15 + a192 * b40 + a36 * b64 + a16 * b200 + a12 * b320 + \
			b1600; c2024 = a2024 + a524 * b6 + a604 * b8 + a42 * b64 + a76 * b88 + a6 * b704 + \
			b2024; c3413 = a3413 + a2024 * b6 + a1394 * b8 + a524 * b15 + a604 * b40 + \
			a91 * b64 + a76 * b200 + a42 * b320 + a6 * b1600 + b3413;
		return { c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
			c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
			c1394, c1600, c2024, c3413 };
	}
	S e() {
		mint c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
			c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
			c1394, c1600, c2024, c3413;
		c6 = 0; c8 = 0; c12 = 0; c15 = 0; c16 = 0; c21 = 0; c36 = 0; c38 = 0; c40 = 0; c42 = 0; c55 = 0; c64 = 0; \
			c76 = 0; c88 = 0; c91 = 0; c96 = 0; c113 = 0; c128 = 0; c192 = 0; c200 = 0; c262 = 0; c264 = 0; \
			c302 = 0; c320 = 0; c433 = 0; c524 = 0; c576 = 0; c604 = 0; c704 = 0; c881 = 0; c1394 = 0; c1600 = \
			0; c2024 = 0; c3413 = 0;
		return { c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
			c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
			c1394, c1600, c2024, c3413 };
	}
	S f_() {
		mint c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
			c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
			c1394, c1600, c2024, c3413;
		c6 = 1; c8 = 0; c12 = 2; c15 = 0; c16 = 0; c21 = 1; c36 = 1; c38 = 0; c40 = 0; c42 = 2; c55 = 0; c64 = 0; \
			c76 = 0; c88 = 0; c91 = 1; c96 = 0; c113 = 0; c128 = 0; c192 = 0; c200 = 0; c262 = 0; c264 = 0; \
			c302 = 0; c320 = 0; c433 = 0; c524 = 0; c576 = 0; c604 = 0; c704 = 0; c881 = 0; c1394 = 0; c1600 = \
			0; c2024 = 0; c3413 = 0;
		return { c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
			c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
			c1394, c1600, c2024, c3413 };
	}
	S g_() {
		mint c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
			c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
			c1394, c1600, c2024, c3413;
		c6 = 0; c8 = 1; c12 = 0; c15 = 0; c16 = 2; c21 = 0; c36 = 0; c38 = 1; c40 = -1; c42 = 0; c55 = 0; c64 = \
			1; c76 = 2; c88 = -1; c91 = 0; c96 = 0; c113 = -1; c128 = 2; c192 = 0; c200 = 1; c262 = 1; c264 = -\
			1; c302 = 0; c320 = -1; c433 = 1; c524 = 2; c576 = 0; c604 = 0; c704 = -1; c881 = -1; c1394 = 0; \
			c1600 = 1; c2024 = -1; c3413 = 1;
		return { c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
			c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
			c1394, c1600, c2024, c3413 };
	}
	auto f = f_();
	auto g = g_();
}


// 自動生成
namespace bbb {
	using S = tuple<mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint, mint>;
	S op(S b, S a) {
		auto [a1604,a1608,a1645,a1690,a1192716,a1270420,a1288925,a1327202,a2505680,\
a2524260,a2585060,a2597320,a128533279,a321880651,a408685132,\
a599669280,a641046429,a642596329,a774556867,a799646519,a834538187,\
a868580847,a887793047] = a;
		auto [b1604,b1608,b1645,b1690,b1192716,b1270420,b1288925,b1327202,b2505680,\
b2524260,b2585060,b2597320,b128533279,b321880651,b408685132,\
b599669280,b641046429,b642596329,b774556867,b799646519,b834538187,\
b868580847,b887793047] = b;
		mint c1604,c1608,c1645,c1690,c1192716,c1270420,c1288925,c1327202,c2505680,\
c2524260,c2585060,c2597320,c128533279,c321880651,c408685132,\
c599669280,c641046429,c642596329,c774556867,c799646519,c834538187,\
c868580847,c887793047;
		c1604=a1604 + b1604;c1608=a1608 + b1608;c1645=a1645 + \
b1645;c1690=a1690 + b1690;c1192716=a1192716 + a1608*b1604 + \
b1192716;c1270420=a1270420 + a1604*b1608 + b1270420;c1288925=a1288925 \
+ a1690*b1645 + b1288925;c1327202=a1327202 + a1604*b1690 + \
b1327202;c2505680=a2505680 + a1645*b1604 + a1604*b1645 + \
b2505680;c2524260=a2524260 + a1645*b1608 + a1608*b1645 + \
b2524260;c2585060=a2585060 + a1690*b1604 + a1604*b1690 + \
b2585060;c2597320=a2597320 + a1690*b1608 + a1608*b1690 + \
b2597320;c128533279=a128533279 + a887793047*b1604 + a834538187*b1645 \
+ a1288925*b1192716 + a1192716*b1288925 + a2597320*b2505680 + \
b128533279 + a1690*b774556867 + \
a1608*b868580847;c321880651=a321880651 + a1327202*b1608 + \
a1270420*b1690 + a1604*b2597320 + b321880651;c408685132=a408685132 + \
a321880651*b1604 + a599669280*b1690 + a1327202*b1192716 + \
a1270420*b2585060 + b408685132 + \
a1604*b834538187;c599669280=a599669280 + a1270420*b1604 + \
a1604*b1192716 + b599669280;c641046429=a641046429 + a799646519*b1604 \
+ a408685132*b1645 + a642596329*b1192716 + a599669280*b1288925 + \
a321880651*b2505680 + a1604*b128533279 + b641046429 + \
a1327202*b774556867 + a1270420*b868580847;c642596329=a642596329 + \
a1327202*b1645 + a1604*b1288925 + b642596329;c774556867=a774556867 + \
a2524260*b1604 + a1192716*b1645 + a1645*b1192716 + a1608*b2505680 + \
b774556867;c799646519=a799646519 + a642596329*b1608 + \
a321880651*b1645 + a1270420*b1288925 + a1327202*b2524260 + b799646519 \
+ a1604*b887793047;c834538187=a834538187 + a2597320*b1604 + \
a1192716*b1690 + a1690*b1192716 + a1608*b2585060 + \
b834538187;c868580847=a868580847 + a1288925*b1604 + a2585060*b1645 + \
a1604*b1288925 + a1690*b2505680 + b868580847;c887793047=a887793047 + \
a1288925*b1608 + a2597320*b1645 + a1608*b1288925 + a1690*b2524260 + \
b887793047;
		return { c1604,c1608,c1645,c1690,c1192716,c1270420,c1288925,c1327202,c2505680,\
c2524260,c2585060,c2597320,c128533279,c321880651,c408685132,\
c599669280,c641046429,c642596329,c774556867,c799646519,c834538187,\
c868580847,c887793047 };
	}
	S e() {
		mint c1604, c1608, c1645, c1690, c1192716, c1270420, c1288925, c1327202, c2505680, \
			c2524260, c2585060, c2597320, c128533279, c321880651, c408685132, \
			c599669280, c641046429, c642596329, c774556867, c799646519, c834538187, \
			c868580847, c887793047;
		return { c1604,c1608,c1645,c1690,c1192716,c1270420,c1288925,c1327202,c2505680,\
c2524260,c2585060,c2597320,c128533279,c321880651,c408685132,\
c599669280,c641046429,c642596329,c774556867,c799646519,c834538187,\
c868580847,c887793047 };
	}
	S f_() {
		mint c1604, c1608, c1645, c1690, c1192716, c1270420, c1288925, c1327202, c2505680, \
			c2524260, c2585060, c2597320, c128533279, c321880651, c408685132, \
			c599669280, c641046429, c642596329, c774556867, c799646519, c834538187, \
			c868580847, c887793047;
		c1604=1;c1608=2;c1645=0;c1690=0;c1192716=1;c1270420=2;c1288925=0;\
c1327202=0;c2505680=0;c2524260=0;c2585060=0;c2597320=0;c128533279=0;\
c321880651=0;c408685132=0;c599669280=1;c641046429=0;c642596329=0;\
c774556867=0;c799646519=0;c834538187=0;c868580847=0;c887793047=0;
		return { c1604,c1608,c1645,c1690,c1192716,c1270420,c1288925,c1327202,c2505680,\
c2524260,c2585060,c2597320,c128533279,c321880651,c408685132,\
c599669280,c641046429,c642596329,c774556867,c799646519,c834538187,\
c868580847,c887793047 };
	}
	S g_() {
		mint c1604, c1608, c1645, c1690, c1192716, c1270420, c1288925, c1327202, c2505680, \
			c2524260, c2585060, c2597320, c128533279, c321880651, c408685132, \
			c599669280, c641046429, c642596329, c774556867, c799646519, c834538187, \
			c868580847, c887793047;
		c1604=0;c1608=0;c1645=1;c1690=2;c1192716=0;c1270420=0;c1288925=1;\
c1327202=2;c2505680=0;c2524260=0;c2585060=0;c2597320=0;c128533279=0;\
c321880651=0;c408685132=0;c599669280=0;c641046429=0;c642596329=1;\
c774556867=0;c799646519=0;c834538187=0;c868580847=0;c887793047=0;
		return { c1604,c1608,c1645,c1690,c1192716,c1270420,c1288925,c1327202,c2505680,\
c2524260,c2585060,c2597320,c128533279,c321880651,c408685132,\
c599669280,c641046429,c642596329,c774556867,c799646519,c834538187,\
c868580847,c887793047 };
	}
	auto f = f_();
	auto g = g_();
}


// (P, Q)=(2,2) だけ例外処理する．これでもしぐっと速くなるなら頑張る．
void Main1() {
	ll n, m, a, b; int p, q;
	cin >> p >> q >> n >> m >> a >> b;

	dump(naive(n + 1, m, a, b, p, q)); dump("-----");

	mint res;

	if (p == 2 && q == 2) {		
		// a < 0 のときは Σi∈[0..n) i^P (-floor((a i + b) / m))^Q を求め，後で (-1)^Q 倍する．
		if (a < 0) b = m - 1 - b;

		ll br = smod(b, m);
		ll bq = (b - br) / m;
		
		// (0, b/m) → (n-1, (a(n-1)+b)/m) の移動に対応する行列積を計算する．
		auto h = multiple_along_line<ll, bbb::S, bbb::op, bbb::e>(n, m, abs(a), br, bbb::f, bbb::g);
		dump(h);

		// (0, 0) → (0, b/m) の移動に対応する行列を右から掛ける．
		mint bq_pow(1);
		res += get<16>(h) * bq_pow;
		bq_pow *= bq;
		res += get<14>(h) * bq_pow;
		bq_pow *= bq;
		res += get<15>(h) * bq_pow;
	}
	else {
		if (a < 0) {
			a = -a;
			b = b - n * a;
			ll R = smod(b, m);
			ll Q = (b - R) / m;

			auto h = multiple_along_line<ll, aaa::S, aaa::op, aaa::e>(n, m, a, R, aaa::f, aaa::g);
			auto [c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
				c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
				c1394, c1600, c2024, c3413] = h;

			mint h00 = 1 + c6, h01 = c38, h02 = c262, h10 = c6 + c15, h11 = c38 + c113, h12 = c262 + c881, h20 = c36 + c55, h21 = c264 + \
				c433, h22 = c2024 + c3413; // , c8, c64, c8 + c40, c64 + c320, c88 + c200, c704 + c1600, 1
			vvm H{
				{h00, h01, h02},
				{h10, h11, h12},
				{h20, h21, h22}
			};

			vm pow_n(p + 1);
			pow_n[0] = 1;
			repi(i, 1, p) pow_n[i] = pow_n[i - 1] * n;

			vm pow_Q(q + 1);
			pow_Q[0] = 1;
			repi(i, 1, q) pow_Q[i] = pow_Q[i - 1] * Q;

			repi(s, 0, p) repi(t, 0, q) {
				auto ans = H[s][t];
				res += fm.bin(p, s) * pow_n[p - s] * (s & 1 ? -1 : 1) * fm.bin(q, t) * pow_Q[q - t] * ans;
			}
		}
		else {
			ll R = smod(b, m);
			ll Q = (b - R) / m;

			auto h = multiple_along_line<ll, aaa::S, aaa::op, aaa::e>(n, m, a, R, aaa::f, aaa::g);
			auto [c6, c8, c12, c15, c16, c21, c36, c38, c40, c42, c55, c64, c76, c88, c91, c96, c113, \
				c128, c192, c200, c262, c264, c302, c320, c433, c524, c576, c604, c704, c881, \
				c1394, c1600, c2024, c3413] = h;

			mint h00 = 1 + c6, h01 = c38, h02 = c262, h10 = c6 + c15, h11 = c38 + c113, h12 = c262 + c881, h20 = c36 + c55, h21 = c264 + \
				c433, h22 = c2024 + c3413; // , c8, c64, c8 + c40, c64 + c320, c88 + c200, c704 + c1600, 1
			vvm H{
				{h00, h01, h02},
				{h10, h11, h12},
				{h20, h21, h22}
			};

			vm pow_Q(q + 1);
			pow_Q[0] = 1;
			repi(i, 1, q) pow_Q[i] = pow_Q[i - 1] * Q;

			repi(t, 0, q) {
				mint ans = H[p][t];
				res += fm.bin(q, t) * pow_Q[q - t] * ans;
			}
		}
	}

	cout << res << "\n";
}


void Main2() {
	ll n, m, a, b; int p, q;
	cin >> p >> q >> n >> m >> a >> b;

	cout << arithmetic_powered_floor_sum<ll, mint>(n + 1, m, a, b, p, q) << "\n";
}


int main() {
	input_from_file("input.txt");
//	output_to_file("output.txt");

	int t = 1;
	cin >> t; // マルチテストケースの場合

	if (t > 5) {
		while (t--) {
			dump("------------------------------");
			Main1();
		}
	}
	else {
		while (t--) {
			dump("------------------------------");
			Main2();
		}
	}
}
0