結果
| 問題 | No.2747 Permutation Adjacent Sum |
| ユーザー |
 ponjuice
|
| 提出日時 | 2024-04-13 18:29:45 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 448 ms / 3,000 ms |
| コード長 | 9,581 bytes |
| コンパイル時間 | 1,719 ms |
| コンパイル使用メモリ | 112,288 KB |
| 最終ジャッジ日時 | 2025-02-21 01:14:02 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 40 |
ソースコード
// O(klogk + √p logp)#include<iostream>#include<vector>#include<cmath>#include<cassert>using namespace std;using ll = long long;template< int mod >struct ModInt {int x;ModInt() : x(0) {}ModInt(ll y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}ModInt &operator*=(const ModInt &p) {x = (int) (1LL * x * p.x % mod);return *this;}ModInt &operator/=(const ModInt &p) {*this *= p.inverse();return *this;}ModInt operator-() const { return ModInt(-x); }ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }bool operator==(const ModInt &p) const { return x == p.x; }bool operator!=(const ModInt &p) const { return x != p.x; }ModInt inverse() const {int a = x, b = mod, u = 1, v = 0, t;while(b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);}return ModInt(u);}ModInt pow(ll n) const {ModInt ret(1), mul(x);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const ModInt &p) {return os << p.x;}friend istream &operator>>(istream &is, ModInt &a) {ll t;is >> t;a = ModInt< mod >(t);return (is);}static int get_mod() { return mod; }ll get(){return x;}};using modint = ModInt<998244353>;template< typename T >struct Combination {vector< T > _fact, _rfact, _inv;Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {_fact[0] = _rfact[sz] = _inv[0] = 1;for(int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;_rfact[sz] /= _fact[sz];for(int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);for(int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];}inline T fact(int k) const { return _fact[k]; }inline T rfact(int k) const { return _rfact[k]; }inline T inv(int k) const { return _inv[k]; }T P(int n, int r) const {if(r < 0 || n < r) return 0;return fact(n) * rfact(n - r);}T C(int p, int q) const {if(q < 0 || p < q) return 0;return fact(p) * rfact(q) * rfact(p - q);}T H(int n, int r) const {if(n < 0 || r < 0) return (0);return r == 0 ? 1 : C(n + r - 1, r);}};template< typename T >T lagrange_polynomial(const vector< T > &y, ll t) {int N = y.size() - 1;Combination< T > comb(N);if(t <= N) return y[t];T ret(0);vector< T > dp(N + 1, 1), pd(N + 1, 1);for(int i = 0; i < N; i++) dp[i + 1] = dp[i] * (t - i);for(int i = N; i > 0; i--) pd[i - 1] = pd[i] * (t - i);for(int i = 0; i <= N; i++) {T tmp = y[i] * dp[i] * pd[i] * comb.rfact(i) * comb.rfact(N - i);if((N - i) & 1) ret -= tmp;else ret += tmp;}return ret;}namespace FastFourierTransform {using real = double;struct C {real x, y;C() : x(0), y(0) {}C(real x, real y) : x(x), y(y) {}inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }inline C conj() const { return C(x, -y); }};const real PI = acosl(-1);int base = 1;vector< C > rts = { {0, 0},{1, 0} };vector< int > rev = {0, 1};void ensure_base(int nbase) {if(nbase <= base) return;rev.resize(1 << nbase);rts.resize(1 << nbase);for(int i = 0; i < (1 << nbase); i++) {rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));}while(base < nbase) {real angle = PI * 2.0 / (1 << (base + 1));for(int i = 1 << (base - 1); i < (1 << base); i++) {rts[i << 1] = rts[i];real angle_i = angle * (2 * i + 1 - (1 << base));rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));}++base;}}void fft(vector< C > &a, int n) {assert((n & (n - 1)) == 0);int zeros = __builtin_ctz(n);ensure_base(zeros);int shift = base - zeros;for(int i = 0; i < n; i++) {if(i < (rev[i] >> shift)) {swap(a[i], a[rev[i] >> shift]);}}for(int k = 1; k < n; k <<= 1) {for(int i = 0; i < n; i += 2 * k) {for(int j = 0; j < k; j++) {C z = a[i + j + k] * rts[j + k];a[i + j + k] = a[i + j] - z;a[i + j] = a[i + j] + z;}}}}vector< ll > multiply(const vector< int > &a, const vector< int > &b) {int need = (int) a.size() + (int) b.size() - 1;int nbase = 1;while((1 << nbase) < need) nbase++;ensure_base(nbase);int sz = 1 << nbase;vector< C > fa(sz);for(int i = 0; i < sz; i++) {int x = (i < (int) a.size() ? a[i] : 0);int y = (i < (int) b.size() ? b[i] : 0);fa[i] = C(x, y);}fft(fa, sz);C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);for(int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;fa[i] = z;}for(int i = 0; i < (sz >> 1); i++) {C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];fa[i] = A0 + A1 * s;}fft(fa, sz >> 1);vector< ll > ret(need);for(int i = 0; i < need; i++) {ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);}return ret;}};template< typename T >struct ArbitraryModConvolution {using real = FastFourierTransform::real;using C = FastFourierTransform::C;ArbitraryModConvolution() = default;vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {if(need == -1) need = a.size() + b.size() - 1;int nbase = 0;while((1 << nbase) < need) nbase++;FastFourierTransform::ensure_base(nbase);int sz = 1 << nbase;vector< C > fa(sz);for(int i = 0; i < (int)a.size(); i++) {fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);}fft(fa, sz);vector< C > fb(sz);if(a == b) {fb = fa;} else {for(int i = 0; i < (int)b.size(); i++) {fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);}fft(fb, sz);}real ratio = 0.25 / sz;C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);for(int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);C a1 = (fa[i] + fa[j].conj());C a2 = (fa[i] - fa[j].conj()) * r2;C b1 = (fb[i] + fb[j].conj()) * r3;C b2 = (fb[i] - fb[j].conj()) * r4;if(i != j) {C c1 = (fa[j] + fa[i].conj());C c2 = (fa[j] - fa[i].conj()) * r2;C d1 = (fb[j] + fb[i].conj()) * r3;C d2 = (fb[j] - fb[i].conj()) * r4;fa[i] = c1 * d1 + c2 * d2 * r5;fb[i] = c1 * d2 + c2 * d1;}fa[j] = a1 * b1 + a2 * b2 * r5;fb[j] = a1 * b2 + a2 * b1;}fft(fa, sz);fft(fb, sz);vector< T > ret(need);for(int i = 0; i < need; i++) {ll aa = llround(fa[i].x);ll bb = llround(fb[i].x);ll cc = llround(fa[i].y);aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;ret[i] = aa + (bb << 15) + (cc << 30);}return ret;}};template< typename T >T factorial(ll n) {if(n >= T::get_mod()) return 0;ArbitraryModConvolution< T > fft;ll d = 1 << 15;Combination< T > comb(2 * d);vector< T > seq({1, d + 1});seq.reserve(d + 1);int sz = 1;while(sz < d) {vector< T > aux(sz, 1), f(sz * 4), g(sz * 4);for(int i = 0; i <= sz; i++) {f[i] = comb.rfact(i) * comb.rfact(sz - i) * seq[i];if(((sz + i) & 1)) f[i] = -f[i];}vector< T > pf(f), as;as.emplace_back(sz + 1);as.emplace_back(T(sz) / d);as.emplace_back(T(sz) / d + sz + 1);for(int idx = 0; idx < 3; idx++) {for(int i = 0; i < sz * 4; i++) f[i] = pf[i];for(int i = 1; i < sz * 2 + 2; i++) g[i] = T(1) / (as[idx] - sz + i - 1);f = fft.multiply(f, g);f.resize(sz * 4);T prod = 1;for(int i = 0; i <= sz; i++) prod *= as[idx] - i;for(int i = 0; i <= sz; i++) {f[sz + i + 1] *= prod;prod *= as[idx] + i + 1;prod /= as[idx] - (sz - i);}if(idx == 0) {for(int i = 0; i < sz; i++) aux[i] = f[sz + i + 1];} else if(idx == 1) {for(int i = 0; i <= sz; i++) seq[i] *= f[sz + i + 1];} else {for(int i = 0; i < sz; i++) aux[i] *= f[sz + i + 1];}}for(auto x : aux) seq.emplace_back(x);sz <<= 1;}T res = 1;ll l = min(d, (n + 1) / d);for(ll i = 0; i < l; i++) res *= seq[i];for(ll i = l * d + 1; i <= n; i++) res *= i;return res;}int main(){ll n,k;cin >> n >> k;ll siz = k + 3;vector<modint> k1(siz,0 ), k2(siz, 0);for(int i = 1; i < siz; i++) {k1[i] = modint(i).pow(k) + k1[i-1];k2[i] = modint(i).pow(k+1) + k2[i-1];}cout << factorial<modint>(n-1) * 2 * (lagrange_polynomial(k1, n) * n - lagrange_polynomial(k2, n)) << endl;}