結果
| 問題 | No.1080 Strange Squared Score Sum |
| ユーザー |
 chocorusk
|
| 提出日時 | 2020-06-12 22:17:46 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,140 ms / 5,000 ms |
| コード長 | 9,058 bytes |
| コンパイル時間 | 3,591 ms |
| コンパイル使用メモリ | 147,396 KB |
| 最終ジャッジ日時 | 2025-01-11 02:39:21 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 20 |
ソースコード
#include <cstdio>#include <cstring>#include <iostream>#include <string>#include <cmath>#include <bitset>#include <vector>#include <map>#include <set>#include <queue>#include <deque>#include <algorithm>#include <complex>#include <unordered_map>#include <unordered_set>#include <random>#include <cassert>#include <fstream>#include <utility>#include <functional>#include <time.h>#include <stack>#include <array>#define popcount __builtin_popcountusing namespace std;typedef long long int ll;typedef pair<int, int> P;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< int64_t > 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< int64_t > 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< int mod >struct ModInt {int x;ModInt() : x(0) {}ModInt(int64_t 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(int64_t 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) {int64_t t;is >> t;a = ModInt< mod >(t);return (is);}static int get_mod() { return mod; }};const ll MOD=1e9+9;using mint = ModInt< MOD >;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 < 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 < 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++) {int64_t aa = llround(fa[i].x);int64_t bb = llround(fb[i].x);int64_t 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;}};ll powmod(ll a, ll k){ll ap=a, ans=1;while(k){if(k&1){ans*=ap;ans%=MOD;}ap=ap*ap;ap%=MOD;k>>=1;}return ans;}ll inv(ll a){return powmod(a, MOD-2);}ArbitraryModConvolution<mint> fft;vector<ll> multiply(vector<ll> a, vector<ll> b){vector<mint> a1(a.size()), b1(b.size());for(int i=0; i<a.size(); i++) a1[i]=mint(a[i]);for(int i=0; i<b.size(); i++) b1[i]=mint(b[i]);auto c1=fft.multiply(a1, b1);vector<ll> c(c1.size());for(int i=0; i<c1.size(); i++) c[i]=c1[i].x;return c;}vector<ll> inverse(vector<ll> a){ll a0=a[0], a0inv=inv(a0);int n=a.size();for(int i=0; i<n; i++) (a[i]*=a0inv)%=MOD;int k=0;while((1<<k)<n) k++;vector<ll> b(1, 1);for(int i=1; i<=k; i++){vector<ll> a1(1<<i);for(int j=0; j<min(1<<i, n); j++) a1[j]=a[j];vector<ll> b1=multiply(b, b);b1=multiply(b1, a1);b.resize(1<<i);for(int j=0; j<(1<<i); j++) b[j]=(2*b[j]-b1[j]+MOD)%MOD;}b.resize(n);for(int i=0; i<n; i++) (b[i]*=a0inv)%=MOD;return b;}vector<ll> log(vector<ll> a){int n=a.size();if(n==1){vector<ll> c(1);return c;}vector<ll> da(n);for(int i=0; i<n-1; i++) da[i]=a[i+1]*(i+1)%MOD;vector<ll> b=inverse(a);vector<ll> c=multiply(da, b);c.resize(n);vector<ll> invs(n);invs[1]=1;for(int i=2; i<n; i++) invs[i]=MOD-invs[MOD%i]*(MOD/i)%MOD;for(int i=n-1; i>=1; i--) c[i]=c[i-1]*invs[i]%MOD;c[0]=0;return c;}vector<ll> exp(vector<ll> a){int n=a.size();int k=0;while((1<<k)<n) k++;vector<ll> b(1, 1);for(int i=1; i<=k; i++){b.resize(1<<i);vector<ll> b1=log(b);for(int j=0; j<(1<<i); j++){b1[j]=MOD-b1[j];if(b1[j]>=MOD) b1[j]-=MOD;}for(int j=0; j<min(n, 1<<i); j++){b1[j]+=a[j];if(b1[j]>=MOD) b1[j]-=MOD;}b1[0]++;if(b1[0]>=MOD) b1[0]-=MOD;b=multiply(b, b1);}b.resize(n);return b;}int main(){int n;cin>>n;const ll I=569522298;vector<ll> f1(n+1), f2(n+1);for(ll i=1; i<=n; i++){f1[i]=(i+1)*(i+1)%MOD*I%MOD;f2[i]=(MOD-f1[i])%MOD;}auto g1=exp(f1), g2=exp(f2);ll fn=1;for(int i=1; i<=n; i++) (fn*=i)%=MOD;for(int i=1; i<=n; i++){cout<<(g1[i]*(1-I+MOD)+g2[i]*(1+I))%MOD*((MOD+1)/2)%MOD*fn%MOD<<endl;}return 0;}