結果

問題 No.3247 Multiplication 8 2
ユーザー 👑 ygussany
提出日時 2025-08-18 09:57:00
言語 C
(gcc 13.3.0)
結果
AC  
実行時間 382 ms / 4,000 ms
コード長 6,946 bytes
コンパイル時間 538 ms
コンパイル使用メモリ 33,968 KB
実行使用メモリ 130,204 KB
最終ジャッジ日時 2025-08-18 09:57:12
合計ジャッジ時間 11,693 ms
ジャッジサーバーID
（参考情報） 		judge1 / 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 * 4
other AC * 28
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ソースコード

diff # 

#include <stdio.h>
#include <stdlib.h>

#define NTT_MAX 22
#define NTT_d_MAX (1 << NTT_MAX)

const int Mod = 998244353,
	bit[24] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608},
	bit_inv[24] = {1, 499122177, 748683265, 873463809, 935854081, 967049217, 982646785, 990445569, 994344961, 996294657, 997269505, 997756929, 998000641, 998122497, 998183425, 998213889, 998229121, 998236737, 998240545, 998242449, 998243401, 998243877, 998244115, 998244234},
	root[24] = {1, 998244352, 911660635, 372528824, 929031873, 452798380, 922799308, 781712469, 476477967, 166035806, 258648936, 584193783, 63912897, 350007156, 666702199, 968855178, 629671588, 24514907, 996173970, 363395222, 565042129, 733596141, 267099868, 15311432},
	root_inv[24] = {1, 998244352, 86583718, 509520358, 337190230, 87557064, 609441965, 135236158, 304459705, 685443576, 381598368, 335559352, 129292727, 358024708, 814576206, 708402881, 283043518, 3707709, 121392023, 704923114, 950391366, 428961804, 382752275, 469870224};

void NTT_inline(int kk, int a[], int x[])
{
	int h, hh, i, ii, j, jj, k, l, r = bit[kk], d = bit[kk-1], tmpp, cur, prev;
	int *pi, *pii, *pj, *pjj;
	static int y[2][NTT_d_MAX];
	long long tmp;
	for (i = 0; i < r; i++) y[0][i] = a[i];
	for (k = 1, kk--, cur = 1, prev = 0; kk >= 0; k++, kk--, cur ^= 1, prev ^= 1) {
		for (h = 0, tmp = 1; h << (kk + 1) < r; h++, tmp = tmp * root[k] % Mod) {
			for (hh = 0, pi = &(y[cur][h<<kk]), pii = pi + d, pj = &(y[prev][h<<(kk+1)]), pjj = pj + bit[kk]; hh < bit[kk]; hh++, pi++, pii++, pj++, pjj++) {
				tmpp = tmp * (*pjj) % Mod;
				*pi = *pj + tmpp;
				if (*pi >= Mod) *pi -= Mod;
				*pii = *pj - tmpp;
				if (*pii < 0) *pii += Mod;
			}
		}
	}
	for (i = 0; i < r; i++) x[i] = y[prev][i];
}

void NTT_reverse_inline(int kk, int a[], int x[])
{
	int h, hh, i, ii, j, jj, k, l, r = bit[kk], d = bit[kk-1], tmpp, cur, prev;
	int *pi, *pii, *pj, *pjj;
	static int y[2][NTT_d_MAX];
	long long tmp;
	for (i = 0; i < r; i++) y[0][i] = a[i];
	for (k = 1, kk--, cur = 1, prev = 0; kk >= 0; k++, kk--, cur ^= 1, prev ^= 1) {
		for (h = 0, tmp = 1; h << (kk + 1) < r; h++, tmp = tmp * root_inv[k] % Mod) {
			for (hh = 0, pi = &(y[cur][h<<kk]), pii = pi + d, pj = &(y[prev][h<<(kk+1)]), pjj = pj + bit[kk]; hh < bit[kk]; hh++, pi++, pii++, pj++, pjj++) {
				tmpp = tmp * (*pjj) % Mod;
				*pi = *pj + tmpp;
				if (*pi >= Mod) *pi -= Mod;
				*pii = *pj - tmpp;
				if (*pii < 0) *pii += Mod;
			}
		}
	}
	for (i = 0; i < r; i++) x[i] = y[prev][i];
}



// Compute c[0-d] = a[0-d] + b[0-d]
void FPS_sum(int d, int a[], int b[], int c[])
{
	int i;
	for (i = 0; i <= d; i++) {
		c[i] = a[i] + b[i];
		if (c[i] >= Mod) c[i] -= Mod;
	}
}

// Compute c[0-d] = a[0-d] - b[0-d]
void FPS_diff(int d, int a[], int b[], int c[])
{
	int i;
	for (i = 0; i <= d; i++) {
		c[i] = a[i] - b[i];
		if (c[i] < 0) c[i] += Mod;
	}
}



#define NTT_THR 70

// Compute c[0-dc] = a[0-da] * b[0-db] (naive)
void FPS_prod_naive(int da, int db, int dc, int a[], int b[], int c[])
{
	int i, j, sa, sb;
	static int supp_a[NTT_d_MAX], supp_b[NTT_d_MAX];
	static long long tmp[NTT_d_MAX];
	for (i = 0, sa = 0; i <= da; i++) if (a[i] != 0) supp_a[sa++] = i;
	for (i = 0, sb = 0; i <= db; i++) if (b[i] != 0) supp_b[sb++] = i;
	for (i = 0; i <= dc; i++) tmp[i] = 0;
	for (i = 0; i < sa; i++) for (j = 0; j < sb && supp_a[i] + supp_b[j] <= dc; j++) tmp[supp_a[i] + supp_b[j]] += (long long)a[supp_a[i]] * b[supp_b[j]] % Mod;
	for (i = 0; i <= dc; i++) c[i] = tmp[i] % Mod;
}

// Compute c[0-dc] = a[0-da] * b[0-db] (NTT)
void FPS_prod_NTT(int da, int db, int dc, int a[], int b[], int c[])
{
	int i, k;
	static int aa[NTT_d_MAX], bb[NTT_d_MAX], cc[NTT_d_MAX];
	for (k = 0; bit[k] <= da + db; k++);
	for (i = 0; i <= da; i++) aa[i] = a[i];
	for (i = da + 1; i < bit[k]; i++) aa[i] = 0;
	for (i = 0; i <= db; i++) bb[i] = b[i];
	for (i = db + 1; i < bit[k]; i++) bb[i] = 0;
	
	static int x[NTT_d_MAX], y[NTT_d_MAX], z[NTT_d_MAX];
	NTT_inline(k, aa, x);
	if (db == da) {
		for (i = 0; i <= da; i++) if (a[i] != b[i]) break;
		if (i <= da) NTT_inline(k, bb, y);
		else for (i = 0; i < bit[k]; i++) y[i] = x[i];
	} else NTT_inline(k, bb, y);
	for (i = 0; i < bit[k]; i++) z[i] = (long long)x[i] * y[i] % Mod;
	NTT_reverse_inline(k, z, cc);
	for (i = 0; i <= dc; i++) c[i] = (long long)cc[i] * bit_inv[k] % Mod;
}

// Compute c[0-dc] = a[0-da] * b[0-db]
void FPS_prod(int da, int db, int dc, int a[], int b[], int c[])
{
	int i, sa, sb;
	if (da > dc) da = dc;
	if (db > dc) db = dc;
	for (i = 0, sa = 0; i <= da && sa <= NTT_THR; i++) if (a[i] != 0) sa++;
	for (i = 0, sb = 0; i <= db && sb <= NTT_THR; i++) if (b[i] != 0) sb++;
	if (sa <= NTT_THR || sb <= NTT_THR) FPS_prod_naive(da, db, dc, a, b, c);
	else FPS_prod_NTT(da, db, dc, a, b, c);
}



long long div_mod(long long x, long long y, long long z)
{
	if (x % y == 0) return x / y;
	else return (div_mod((1 + x / y) * y - x, (z % y), y) * z + x) / y;
}

long long pow_mod(int n, long long k)
{
	long long N, ans = 1;
	for (N = n; k > 0; k >>= 1, N = N * N % Mod) if (k & 1) ans = ans * N % Mod;
	return ans;
}



int main()
{
	int i, N, K, A[1000001];
	if (scanf("%d %d", &N, &K) != 2) return -1;
	if (N < 1 || N > 888000 || K < 1 || K > 888000000) return -1;
	for (i = 1; i <= N; i++) {
		if (scanf("%d", &(A[i])) != 1) return -1;
		if (A[i] != 1 && A[i] != 2 && A[i] != -1 && A[i] != -2) return -1;
	}
	if (scanf("%d", &N) != EOF) return -1;
	
	int j, k, flag[1000001] = {1}, num[1000001] = {0, 1};
	for (i = 1, j = 1, k = 1; i <= N; i++) {
		k *= A[i];
		if (k == 1 && j > 1) {
			flag[i] = j;
			num[j]++;
		} else if (k == 8) {
			flag[i] = ++j;
			num[j]++;
			k = 1;
		}
	}
	if (j == 1 || k != 1) {
		printf("0\n");
		return 0;
	}
	for (i = 1; i < N; i++) {
		if (flag[i] == j) {
			flag[i] = 0;
			num[j]--;
		}
	}
	
	int *x[1000000];
	long long prod = 1;
	for (i = 1; i <= j; i++) {
		prod = prod * num[i] % Mod;
		x[i] = (int*)malloc(sizeof(int) * (num[i] + 1));
		num[i] = 0;
	}
	for (i = 0; i <= N; i++) {
		if (flag[i] == 0) continue;
		x[flag[i]][++num[flag[i]]] = i;
	}
	
	int jj, a[2097152], b[2097152], c[2097152], d[2], w;
	long long ans = 0, pow[1000001];
	for (i = 1; i <= N; i++) pow[i] = pow_mod(i, K);
	for (jj = 1; jj < j; jj++) {
		w = x[jj+1][1] - x[jj][num[jj]];
		d[0] = x[jj][num[jj]] - x[jj][1];
		d[1] = x[jj+1][num[jj+1]] - x[jj+1][1];
		for (i = 0; i <= d[0]; i++) a[i] = 0;
		for (i = 0; i <= d[1]; i++) b[i] = 0;
		for (i = 1; i <= num[jj]; i++) a[x[jj][num[jj]] - x[jj][i]] = 1;
		for (i = 1; i <= num[jj+1]; i++) b[x[jj+1][i] - x[jj+1][1]] = 1;
		
		FPS_prod(d[0], d[1], d[0] + d[1], a, b, c);
		prod = div_mod(prod, (long long)num[jj] * num[jj+1] % Mod, Mod);
		for (i = 0; i <= d[0] + d[1]; i++) if (c[i] != 0) ans += pow[w+i] * prod % Mod * c[i] % Mod;
		prod = prod * num[jj] % Mod * num[jj+1] % Mod;
	}
	printf("%lld\n", ans % Mod);
	fflush(stdout);
	return 0;
}
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