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;
}

inline uint Mod_mult(const uint x, const uint y) // 32-bit computing
{
	unsigned long long t = (unsigned long long) x*y;
unsigned int u = t * 1.0017587347173304e-9;
	return (unsigned int)t-u*Mod;
}

struct Z
{
	uint v;
	Z() { }
	Z(const uint _v) : v(_v) { }
};

inline Z operator+(const Z &x1, const Z &x2) { return x1.v + x2.v < Mod ? x1.v + x2.v : x1.v + x2.v - Mod; }
inline Z operator-(const Z &x1, const Z &x2) { return x1.v >= x2.v ? x1.v - x2.v : x1.v + Mod - x2.v; }
inline Z operator*(const Z &x1, const Z &x2) { return Mod_mult(x1.v, x2.v); }
inline Z &operator*=(Z &x1, const Z &x2) { x1.v = Mod_mult(x1.v, x2.v); return x1; }

Z Power(Z Base, int Exp)
{
	Z res = 1;
	for (; Exp; Base *= Base, Exp >>= 1)
		if (Exp & 1)
			res *= Base;
	return res;
}

inline uint mf(uint x)
{
	return (static_cast<uint64>(x) << 32) / Mod;
}

int size;
uint w[Max_size], w_q[Max_size];

inline uint mult_Shoup_2(const uint x, const uint y, const uint y_q)
{
	uint q = static_cast<uint64>(x) * y_q >> 32;
	return x * y - q * Mod;
}

inline uint mult_Shoup(const uint x, const uint y, const uint y_q)
{
	return norm(mult_Shoup_2(x, y, y_q));
}

inline uint mult_Shoup_q(const uint x, const uint y, const uint y_q)
{
	uint q = static_cast<uint64>(x) * y_q >> 32;
	return q + (x * y - q * Mod >= Mod);
}

inline void init(int n)
{
	for (size = 2; size < n; size <<= 1)
		;
	uint pr = Power(g, (Mod - 1) / size).v;
	uint pr_q = (static_cast<uint64>(pr) << 32) / Mod;
	uint pr_r = (static_cast<uint64>(pr) << 32) % Mod;
	size >>= 1;
	w[size] = 1, w_q[size] = (static_cast<uint64>(w[size]) << 32) / Mod;
//	for (int i = 1; i != size; ++i)
//		w[size + i] = mult_Shoup(w[size + i - 1], pr, pr_q), w_q[size + i] = (static_cast<uint64>(w[size + i]) << 32) / Mod;
#define compute(r, r_q, b, b_q)\
	do\
	{\
		uint x = b;\
		uint64 p = static_cast<uint64>(x) * pr_q;\
		uint q = p >> 32;\
		r = norm(x * pr - q * Mod);\
		r_q = static_cast<uint>(p) + mult_Shoup_q(pr_r, b, b_q);\
	} while (0)
	if (size <= 4)
	{
		for (int i = 1; i != size; ++i)
			compute(w[size + i], w_q[size + i], w[size + i - 1], w_q[size + i - 1]);
	}
	else
	{
		for (int i = 1; i != 8; ++i)
			compute(w[size + i], w_q[size + i], w[size + i - 1], w_q[size + i - 1]);
		pr = w[size + 4], pr_q = w_q[size + 4], pr_r = -pr_q * Mod;
		for (int i = 8; i != size; i += 4)
		{
			compute(w[size + i + 0], w_q[size + i + 0], w[size + i - 4], w_q[size + i - 4]);
			compute(w[size + i + 1], w_q[size + i + 1], w[size + i - 3], w_q[size + i - 3]);
			compute(w[size + i + 2], w_q[size + i + 2], w[size + i - 2], w_q[size + i - 2]);
			compute(w[size + i + 3], w_q[size + i + 3], w[size + i - 1], w_q[size + i - 1]);
		} 
	}
	for (int i = size - 1; i; --i)
		w[i] = w[i * 2], w_q[i] = w_q[i * 2];
	size <<= 1;
}

inline void DFT_fr_2(Z _A[], const int L)
{
	if (L == 1)
		return;
	uint *A = reinterpret_cast<uint *>(_A);
//	auto butterfly1 = [](uint &a, uint &b)
//	{
//		uint x = norm_2(a + b), y = norm_2(a + Mod * 2 - b);
//		a = x, b = y;
//	};
#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;
	}
//	auto butterfly = [](uint &a, uint &b, const uint _w, const uint _w_q)
//	{
//		uint x = norm_2(a + b), y = mult_Shoup_2(a + Mod * 2 - b, _w, _w_q);
//		a = x, b = y;
//	};
#define butterfly(a, b, _w, _w_q)\
	do\
	{\
		uint _a = a, _b = b;\
		uint x = norm_2(_a + _b), y = mult_Shoup_2(_a + Mod * 2 - _b, _w, _w_q);\
		a = x, b = y;\
	} while (0)
	if (L == 4)
	{
		butterfly1(A[0], A[2]);
		butterfly(A[1], A[3], w[3], w_q[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[d + j + 0], w_q[d + j + 0]);
				butterfly(A[i + j + 1], A[i + d + j + 1], w[d + j + 1], w_q[d + j + 1]);
				butterfly(A[i + j + 2], A[i + d + j + 2], w[d + j + 2], w_q[d + j + 2]);
				butterfly(A[i + j + 3], A[i + d + j + 3], w[d + j + 3], w_q[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[5], w_q[5]);
		butterfly(A[i + 2], A[i + 6], w[6], w_q[6]);
		butterfly(A[i + 3], A[i + 7], w[7], w_q[7]);
	}
	for (int i = 0; i != L; i += 8)
	{
		butterfly1(A[i + 0], A[i + 2]);
		butterfly(A[i + 1], A[i + 3], w[3], w_q[3]);
		butterfly1(A[i + 4], A[i + 6]);
		butterfly(A[i + 5], A[i + 7], w[3], w_q[3]);
	}
	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]);
	}
#undef butterfly1
#undef butterfly
}

inline void IDFT_fr(Z _A[], const int L)
{
	if (L == 1)
		return;
	uint *A = reinterpret_cast<uint *>(_A);
//	auto butterfly1 = [](uint &a, uint &b)
//	{
//		uint x = norm_2(a), t = norm_2(b);
//		a = x + t, b = x + Mod * 2 - t;
//	};
#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;
	}
//	auto butterfly = [](uint &a, uint &b, const uint _w, const uint _w_q)
//	{
//		uint x = norm_2(a), t = mult_Shoup_2(b, _w, _w_q);
//		a = x + t, b = x + Mod * 2 - t;
//	};
#define butterfly(a, b, _w, _w_q)\
	do\
	{\
		uint _a = a, _b = b;\
		uint x = norm_2(_a), t = mult_Shoup_2(_b, _w, _w_q);\
		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[3], w_q[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]);
	}
	for (int i = 0; i != L; i += 8)
	{
		butterfly1(A[i + 0], A[i + 2]);
		butterfly(A[i + 1], A[i + 3], w[3], w_q[3]);
		butterfly1(A[i + 4], A[i + 6]);
		butterfly(A[i + 5], A[i + 7], w[3], w_q[3]);
	}
	for (int i = 0; i != L; i += 8)
	{
		butterfly1(A[i + 0], A[i + 4]);
		butterfly(A[i + 1], A[i + 5], w[5], w_q[5]);
		butterfly(A[i + 2], A[i + 6], w[6], w_q[6]);
		butterfly(A[i + 3], A[i + 7], w[7], w_q[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[d + j + 0], w_q[d + j + 0]);
				butterfly(A[i + j + 1], A[i + d + j + 1], w[d + j + 1], w_q[d + j + 1]);
				butterfly(A[i + j + 2], A[i + d + j + 2], w[d + j + 2], w_q[d + j + 2]);
				butterfly(A[i + j + 3], A[i + d + j + 3], w[d + j + 3], w_q[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(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