代码

#include <algorithm>
#include <cstring>
typedef unsigned int uint;
typedef long long unsigned int uint64;
constexpr uint Max_size = 1 << 21 | 5;
constexpr uint g = 3, Mod = 998244353;
inline uint norm_2(const uint x) {
	return x < Mod * 2 ? x : x - Mod * 2;
}
inline uint norm(const uint x) {
	return x < Mod ? x : x - Mod;
}
struct Z {
	uint v;
	Z() { }
	Z(const uint _v) : v(_v) { }
};
inline Z operator+(const Z x1, const Z x2) {
	return norm(x1.v + x2.v);
}
inline Z operator-(const Z x1, const Z x2) {
	return norm(x1.v + Mod - x2.v);
}
inline Z operator-(const Z x) {
	return x.v ? Mod - x.v : 0;
}
inline Z operator*(const Z x1, const Z x2) {
	return static_cast<uint64>(x1.v) * x2.v % Mod;
}
inline Z &operator+=(Z &x1, const Z x2) {
	return x1 = x1 + x2;
}
inline Z &operator-=(Z &x1, const Z x2) {
	return x1 = x1 - x2;
}
inline Z &operator*=(Z &x1, const Z x2) {
	return x1 = x1 * x2;
}
Z Power(Z Base, int Exp) {
	Z res = 1;
	for (; Exp; Base *= Base, Exp >>= 1)
		if (Exp & 1)
			res *= Base;
	return res;
}
int size;
std::pair<uint, uint> w_p[Max_size];
inline uint mult_Shoup_2(const uint x, const std::pair<uint, uint> y_p) {
	uint q = static_cast<uint64>(x) * y_p.second >> 32;
	return x * y_p.first - q * Mod;
}
inline uint mult_Shoup(const uint x, const std::pair<uint, uint> y_p) {
	return norm(mult_Shoup_2(x, y_p));
}
inline uint mult_Shoup_q(const uint x, const std::pair<uint, uint> y_p) {
	uint q = static_cast<uint64>(x) * y_p.second >> 32;
	return q + (x * y_p.first - q * Mod >= Mod);
}
void init_w(const int n) {
	for (size = 2; size < n; size <<= 1)
		;
	uint pr = Power(g, (Mod - 1) / size).v;
	std::pair<uint, uint> pr_p = {pr, (static_cast<uint64>(pr) << 32) / Mod};
	uint pr_r = (static_cast<uint64>(pr) << 32) % Mod;
	size >>= 1;
	w_p[size] = {1, (1ULL << 32) / Mod};
#define compute(r_p, b_p)\
	do\
	{\
		uint x = b_p.first;\
		uint64 p = static_cast<uint64>(x) * pr_p.second;\
		uint q = p >> 32;\
		r_p = {norm(x * pr_p.first - q * Mod), static_cast<uint>(p) + mult_Shoup_q(pr_r, b_p)};\
	} while (0)
	if (size <= 4) {
		for (int i = 1; i != size; ++i)
			compute(w_p[size + i], w_p[size + i - 1]);
	} else {
		for (int i = 1; i != 8; ++i)
			compute(w_p[size + i], w_p[size + i - 1]);
		pr_p = w_p[size + 4], pr_r = -pr_p.second * Mod;
		for (int i = 8; i != size; i += 4) {
			compute(w_p[size + i + 0], w_p[size + i - 4]);
			compute(w_p[size + i + 1], w_p[size + i - 3]);
			compute(w_p[size + i + 2], w_p[size + i - 2]);
			compute(w_p[size + i + 3], w_p[size + i - 1]);
		}
	}
	for (int i = size - 1; i; --i)
		w_p[i] = w_p[i * 2];
	size <<= 1;
}
void DFT_fr_2(Z _A[], const int L) {
	if (L == 1)
		return;
	uint *A = reinterpret_cast<uint *>(_A);
#define butterfly1(a, b)\
	do\
	{\
		uint _a = a, _b = b;\
		uint x = norm_2(_a + _b), y = norm_2(_a + Mod * 2 - _b);\
		a = x, b = y;\
	} while (0)
	if (L == 2) {
		butterfly1(A[0], A[1]);
		return;
	}
#define butterfly(a, b, _w_p)\
	do\
	{\
		uint _a = a, _b = b;\
		uint x = norm_2(_a + _b), y = mult_Shoup_2(_a + Mod * 2 - _b, _w_p);\
		a = x, b = y;\
	} while (0)
	if (L == 4) {
		butterfly1(A[0], A[2]);
		butterfly(A[1], A[3], w_p[3]);
		butterfly1(A[0], A[1]);
		butterfly1(A[2], A[3]);
		return;
	}
	for (int d = L >> 1; d != 4; d >>= 1)
		for (int i = 0; i != L; i += d << 1)
			for (int j = 0; j != d; j += 4) {
				butterfly(A[i + j + 0], A[i + d + j + 0], w_p[d + j + 0]);
				butterfly(A[i + j + 1], A[i + d + j + 1], w_p[d + j + 1]);
				butterfly(A[i + j + 2], A[i + d + j + 2], w_p[d + j + 2]);
				butterfly(A[i + j + 3], A[i + d + j + 3], w_p[d + j + 3]);
			}
	for (int i = 0; i != L; i += 8) {
		butterfly1(A[i + 0], A[i + 4]);
		butterfly(A[i + 1], A[i + 5], w_p[5]);
		butterfly(A[i + 2], A[i + 6], w_p[6]);
		butterfly(A[i + 3], A[i + 7], w_p[7]);
		butterfly1(A[i + 0], A[i + 2]);
		butterfly(A[i + 1], A[i + 3], w_p[3]);
		butterfly1(A[i + 4], A[i + 6]);
		butterfly(A[i + 5], A[i + 7], w_p[3]);
		butterfly1(A[i + 0], A[i + 1]);
		butterfly1(A[i + 2], A[i + 3]);
		butterfly1(A[i + 4], A[i + 5]);
		butterfly1(A[i + 6], A[i + 7]);
	}
#undef butterfly1
#undef butterfly
}
void DFT_fr(Z _A[], const int L) {
	DFT_fr_2(_A, L);
	for (int i = 0; i != L; ++i)_A[i] = norm(_A[i].v);
}
void IDFT_fr(Z _A[], const int L) {
	if (L == 1)
		return;
	uint *A = reinterpret_cast<uint *>(_A);
#define butterfly1(a, b)\
	do\
	{\
		uint _a = a, _b = b;\
		uint x = norm_2(_a), t = norm_2(_b);\
		a = x + t, b = x + Mod * 2 - t;\
	} while (0)
	if (L == 2) {
		butterfly1(A[0], A[1]);
		A[0] = norm(norm_2(A[0])), A[0] = A[0] & 1 ? A[0] + Mod : A[0], A[0] /= 2;
		A[1] = norm(norm_2(A[1])), A[1] = A[1] & 1 ? A[1] + Mod : A[1], A[1] /= 2;
		return;
	}
#define butterfly(a, b, _w_p)\
	do\
	{\
		uint _a = a, _b = b;\
		uint x = norm_2(_a), t = mult_Shoup_2(_b, _w_p);\
		a = x + t, b = x + Mod * 2 - t;\
	} while (0)
	if (L == 4) {
		butterfly1(A[0], A[1]);
		butterfly1(A[2], A[3]);
		butterfly1(A[0], A[2]);
		butterfly(A[1], A[3], w_p[3]);
		std::swap(A[1], A[3]);
		for (int i = 0; i != L; ++i) {
			uint64 m = -A[i] & 3;
			A[i] = norm((A[i] + m * Mod) >> 2);
		}
		return;
	}
	for (int i = 0; i != L; i += 8) {
		butterfly1(A[i + 0], A[i + 1]);
		butterfly1(A[i + 2], A[i + 3]);
		butterfly1(A[i + 4], A[i + 5]);
		butterfly1(A[i + 6], A[i + 7]);
		butterfly1(A[i + 0], A[i + 2]);
		butterfly(A[i + 1], A[i + 3], w_p[3]);
		butterfly1(A[i + 4], A[i + 6]);
		butterfly(A[i + 5], A[i + 7], w_p[3]);
		butterfly1(A[i + 0], A[i + 4]);
		butterfly(A[i + 1], A[i + 5], w_p[5]);
		butterfly(A[i + 2], A[i + 6], w_p[6]);
		butterfly(A[i + 3], A[i + 7], w_p[7]);
	}
	for (int d = 8; d != L; d <<= 1)
		for (int i = 0; i != L; i += d << 1)
			for (int j = 0; j != d; j += 4) {
				butterfly(A[i + j + 0], A[i + d + j + 0], w_p[d + j + 0]);
				butterfly(A[i + j + 1], A[i + d + j + 1], w_p[d + j + 1]);
				butterfly(A[i + j + 2], A[i + d + j + 2], w_p[d + j + 2]);
				butterfly(A[i + j + 3], A[i + d + j + 3], w_p[d + j + 3]);
			}
#undef butterfly1
#undef butterfly
	std::reverse(A + 1, A + L);
	int k = __builtin_ctz(L);
	for (int i = 0; i != L; ++i) {
		uint64 m = -A[i] & (L - 1);
		A[i] = norm((A[i] + m * Mod) >> k);
	}
}
Z A[Max_size], B[Max_size];
void poly_multiply(uint _A[], int N, uint _B[], int M, uint _C[]) {
	memcpy(reinterpret_cast<uint *>(A), _A, (N + 1) * sizeof(uint));
	memcpy(reinterpret_cast<uint *>(B), _B, (M + 1) * sizeof(uint));
	int L;
	for (L = 2; L <= N + M; L <<= 1)
		;
	init_w(L);
	DFT_fr_2(A, L), DFT_fr_2(B, L);
	for (int i = 0; i != L; ++i)
		A[i] *= B[i];
	IDFT_fr(A, L);
	memcpy(_C, reinterpret_cast<uint *>(A), (N + M + 1) * sizeof(uint));
}

评测结果