結果

問題 No.1080 Strange Squared Score Sum
ユーザー chocoruskchocorusk
提出日時 2020-06-12 22:17:46
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 911 ms / 5,000 ms
コード長 9,058 bytes
コンパイル時間 2,223 ms
コンパイル使用メモリ 152,412 KB
実行使用メモリ 34,120 KB
最終ジャッジ日時 2024-06-24 05:12:54
合計ジャッジ時間 13,437 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 438 ms
18,916 KB
testcase_03 AC 863 ms
32,648 KB
testcase_04 AC 202 ms
11,076 KB
testcase_05 AC 213 ms
11,160 KB
testcase_06 AC 47 ms
6,944 KB
testcase_07 AC 98 ms
7,380 KB
testcase_08 AC 425 ms
18,928 KB
testcase_09 AC 409 ms
18,324 KB
testcase_10 AC 47 ms
6,940 KB
testcase_11 AC 841 ms
33,056 KB
testcase_12 AC 413 ms
18,308 KB
testcase_13 AC 880 ms
33,320 KB
testcase_14 AC 424 ms
18,300 KB
testcase_15 AC 2 ms
6,940 KB
testcase_16 AC 911 ms
34,120 KB
testcase_17 AC 452 ms
19,072 KB
testcase_18 AC 458 ms
19,080 KB
testcase_19 AC 457 ms
19,080 KB
testcase_20 AC 862 ms
33,148 KB
testcase_21 AC 863 ms
33,060 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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_popcount
using 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;
}
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