1 条题解
-
0

#include <bits/stdc++.h> #define EB emplace_back #define lg2(x) (31 - __builtin_clz(x)) const int N = 135400, mod = 998244353, half_mod = (mod + 1) / 2, root = 31; typedef long long ll; typedef std::vector <int> vector; typedef int vec[N], *pvec; vec fact, inv, finv; inline int & reduce(int &x) {return x += (x >> 31 & mod);} inline ll & reduce(ll &x) {return x += (x >> 63 & mod);} inline int & half(int &x) {return x = (x >> 1) + (-(x & 1) & half_mod);} inline ll & half(ll &x) {return x = (x >> 1) + (-(x & 1) & half_mod);} inline int & neg(int &x) {return x = (!x - 1) & (mod - x);} inline ll & neg(ll &x) {return x = (!x - 1) & (mod - x);} ll PowerMod(ll a, int n, ll c = 1) {for (; n; n >>= 1, a = a * a % mod) if (n & 1) c = c * a % mod; return c;} void init() { int i; for (inv[1] = 1, i = 2; i < N; ++i) inv[i] = (ll)(mod - mod / i) * inv[mod % i] % mod; for (*finv = *fact = i = 1; i < N; ++i) fact[i] = (ll)fact[i - 1] * i % mod, finv[i] = (ll)finv[i - 1] * inv[i] % mod; } namespace Poly { int l, n; vec rev, x, y; void NTT_init(int len) { if (l == len) return; n = 1 << (l = len); ll g = PowerMod(root, 1 << (23 - l)); *x = 1, *rev = 0; for (int i = 1; i < n; ++i) x[i] = x[i - 1] * g % mod, rev[i] = rev[i >> 1] >> 1 | (i & 1) << (l - 1); } void DNTT(int *d, int *t) { int i, *j, *k, len = 1, delta = n, R; for (i = 0; i < n; ++i) t[rev[i]] = d[i]; for (i = 0; i < l; ++i) { delta >>= 1; for (k = x, j = y; j < y + len; k += delta, ++j) *j = *k; for (j = t; j < t + n; j += len << 1) for (k = j; k < j + len; ++k) { R = (ll)y[k - j] * k[len] % mod; k[len] = (*k - R < 0 ? *k - R + mod : *k - R); *k = (*k + R >= mod ? *k + R - mod : *k + R); } len <<= 1; } } vec B1, B2, B3, B4, B5, B6, B7; void Mul(int deg, pvec a, pvec b, pvec c) { if (!deg) {*c = (ll)*a * *b % mod; return;} NTT_init(lg2(deg) + 1); int i; ll iv = mod - (mod - 1) / n; DNTT(a, c), DNTT(b, B1); for (i = 0; i < n; ++i) B1[i] = (ll)B1[i] * c[i] % mod; DNTT(B1, c), std::reverse(c + 1, c + n); for (i = 0; i < n; ++i) c[i] = c[i] * iv % mod; } void Inv(int deg, pvec a, pvec b) { int len, i; ll iv = half_mod; *b = PowerMod(*a, mod - 2), b[1] = 0; *B1 = *a, B1[1] = a[1]; for (len = 0; 1 << len < deg; ++len) { NTT_init(len + 2); for (i = n >> 1; i < n; ++i) b[i] = B1[i] = 0; DNTT(b, B2), DNTT(B1, B3); for (i = 0; i < n; ++i) reduce(B2[i] = B2[i] * (2ll - (ll)B2[i] * B3[i] % mod) % mod); DNTT(B2, B3), std::reverse(B3 + 1, B3 + n), half(iv); for (i = 0; i < n >> 1; ++i) b[i] = B3[i] * iv % mod; for (; i < n; ++i) b[i] = 0, B1[i] = a[i]; } } void Mul(vector &a, vector &b, vector &ret) { int degA = a.size() - 1, degB = b.size() - 1; if (!(degA || degB)) {ret.emplace_back((ll)a[0] * b[0] % mod); return;} NTT_init(lg2(degA + degB) + 1); int i; ll iv = mod - (mod - 1) / n; memcpy(B1, a.data(), (degA + 1) << 2), memset(B1 + (degA + 1), 0, (n - degA - 1) << 2); memcpy(B2, b.data(), (degB + 1) << 2), memset(B2 + (degB + 1), 0, (n - degB - 1) << 2); DNTT(B1, B3), DNTT(B2, B1); for (i = 0; i < n; ++i) B1[i] = (ll)B1[i] * B3[i] % mod; DNTT(B1, B3), std::reverse(B3 + 1, B3 + n); ret.clear(), ret.reserve(degA + degB + 1); for (i = 0; i <= degA + degB; ++i) ret.EB(B3[i] * iv % mod); } void Diff(int deg, vec a, vec b) {for (int i = 1; i <= deg; ++i) b[i - 1] = (ll)a[i] * i % mod;} void Intg(int deg, vec a, vec b, int ct = 0) {for (int i = 1; i <= deg; ++i) b[i] = (ll)a[i - 1] * inv[i] % mod, *b = ct;} void Ln(int deg, vec a, vec b, bool need_reintegrate = true) { deg -= need_reintegrate, assert(deg); int i, j = deg * 2 - 1; NTT_init(lg2(j) + 1); Diff(deg, a, B4), Inv(deg, a, B5); for (i = deg; i < n; ++i) B4[i] = B5[i] = 0; Mul(j, B4, B5, B6); if (need_reintegrate) Intg(deg, B6, b); else memcpy(b, B6, deg << 2); } void Exp(int deg, vec a, vec b) { int len, i, n = 2; *b = 1, b[1] = 0; for (len = 0; 1 << len < deg; ++len, n <<= 1) { Ln(n, b, B7); *B7 = 1; for (i = 1; i < n; ++i) reduce(B7[i] = a[i] - B7[i]); for (; i < n << 1; ++i) B7[i] = b[i] = 0; Mul((n << 1) - 1, b, B7, B6); for (i = 0; i < n; ++i) b[i] = B6[i]; for (; i < n << 1; ++i) b[i] = 0; } } } int n, K, cnt; vec A, B, invA, lnA; vec a, F, G, lhs, rhs; vector g[N]; int solve(int L, int R) { if (L + 1 == R) return L; int M = (L + R) / 2, id = cnt++, lp = solve(L, M), rp = solve(M, R); return Poly::Mul(g[lp], g[rp], g[id]), id; } void calc_deg_sum() { int i, id; for (i = 0; i < n; ++i) g[i].EB(1), g[i].EB(mod - a[i]); cnt = n, id = solve(0, n); memcpy(G, g[id].data(), (n + 1) << 2); Poly::Ln(n, G, F + 1, false); for (*F = n, i = 1; i <= n; ++i) neg(F[i]); } int main() { int i, j, ans = 0; scanf("%d%d", &n, &K), init(); for (i = 0; i < n; ++i) scanf("%d", a + i); if (n <= 1) return putchar(48 + !K), putchar(10), 0; if (n == 2) return printf("%lld\n", 2ll * *a * a[1] % mod); calc_deg_sum(); for (i = 0; i < n - 1; ++i) A[i] = PowerMod(i + 1, K, finv[i]), B[i] = PowerMod(i + 1, 2 * K, finv[i]); Poly::Ln(n, A, lnA), lnA[n - 1] = 0; memcpy(invA, Poly::B5, (n - 1) << 2); for (i = 0; i < n - 1; ++i) lnA[i] = (ll)lnA[i] * F[i] % mod; Poly::Exp(n - 1, lnA, rhs); Poly::Mul(2 * (n - 2), B, invA, lhs); for (i = 0; i < n - 1; ++i) lhs[i] = (ll)lhs[i] * F[i] % mod; for (i = 0, j = n - 2; i < n - 1; ++i, --j) ans = (ans + (ll)lhs[i] * rhs[j]) % mod; for (i = 0; i < n; ++i) ans = (ll)ans * a[i] % mod; printf("%lld\n", (ll)ans * fact[n - 2] % mod); return 0; }
- 1
信息
- ID
- 4713
- 时间
- 5000ms
- 内存
- 1024MiB
- 难度
- 10
- 标签
- 递交数
- 1
- 已通过
- 1
- 上传者