結果
| 問題 |
No.93 ペガサス
|
| コンテスト | |
| ユーザー |
 Elegia Inferno
|
| 提出日時 | 2020-11-16 15:14:09 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 5,798 bytes |
| コンパイル時間 | 1,455 ms |
| コンパイル使用メモリ | 114,740 KB |
| 実行使用メモリ | 27,788 KB |
| 最終ジャッジ日時 | 2024-07-23 01:32:04 |
| 合計ジャッジ時間 | 2,577 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 15 WA * 1 |
ソースコード
#include <cassert>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cctype>
#include <algorithm>
#include <random>
#include <bitset>
#include <queue>
#include <functional>
#include <set>
#include <map>
#include <vector>
#include <chrono>
#include <iostream>
#include <limits>
#include <numeric>
#define LOG(FMT...) fprintf(stderr, FMT)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int ui;
const int N = 2010;
int n;
int fac[N];
int f[N][N];
struct Solver {
ui MOD;
virtual void setMOD(ui MOD) { this->MOD = MOD; }
int norm(int x) { return x >= MOD ? x - MOD : x; }
void add(int &x, int y) {
if ((x += y - MOD) < 0) x += MOD;
}
void sub(int &x, int y) {
if ((x -= y) < 0) x += MOD;
}
virtual int query(int k) = 0;
};
struct Solver2 : Solver {
int l;
void setMOD(ui MOD) {
Solver::setMOD(MOD);
l = n;
for (int i = 1; i <= n; ++i)
if (fac[i] % MOD == 0) {
l = i - 1;
break;
}
}
vector<ui> mul(const vector<ui> &a, const vector<ui> &b) {
vector<ui> vec(l + 1);
for (int i = 0; i <= l; ++i)
for (int j = 0; j <= i; ++j)
vec[i] += a[j] * b[i - j];
return vec;
}
vector<ui> qmul(const vector<ui> &a, int k) {
if (k == 0) {
vector<ui> id(l + 1);
id[0] = 1;
return id;
}
auto ret = qmul(mul(a, a), k >> 1);
if (k & 1)
ret = mul(ret, a);
return ret;
}
int query(int k) {
if (MOD == 1) return 0;
int t1 = n / k, t2 = n / k + 1,
c2 = n % k, c1 = k - c2;
vector<ui> f1(f[t1], f[t1] + l + 1), f2(f[t2], f[t2] + l + 1);
auto res = mul(qmul(f1, c1), qmul(f2, c2));
ui ret = 0;
for (int i = 0; i <= l; ++i)ret += ui(fac[i]) * res[i];
return ret % MOD;
}
};
static ui MD, INV, R2;
struct SolverOdd : Solver {
int nv2;
int mpow(int x, int k) {
if (k == 0)return 1;
int ret = mpow(x * (ull) x % MOD, k >> 1);
if (k & 1)
ret = ret * (ull) x % MOD;
return ret;
}
static ui reduce(ull x) {
ui y = ui(x >> 32) - ui((ull(ui(x) * INV) * MD) >> 32);
return int(y) < 0 ? y + MD : y;
}
struct Mont {
ui x_;
Mont() : x_(0) {}
Mont(ui x) : x_(reduce(ull(x) * R2)) {}
Mont &operator+=(Mont rhs) {
x_ += rhs.x_ - MD;
if (int(x_) < 0)x_ += MD;
return *this;
}
Mont operator+(Mont rhs) const { return Mont(*this) += rhs; }
Mont &operator*=(Mont rhs) {
x_ = reduce(ull(x_) * rhs.x_);
return *this;
}
Mont operator*(Mont rhs) const { return Mont(*this) *= rhs; }
Mont operator-=(Mont rhs) {
x_ -= rhs.x_;
if (int(x_) < 0)x_ += MD;
return *this;
}
ui get() const { return reduce(x_); }
};
Mont C[N][N];
void setMOD(ui MOD) {
Solver::setMOD(MOD);
MD = MOD;
INV = MOD;
for (int rep = 0; rep < 4; ++rep) INV *= 2 - INV * MOD;
R2 = -ull(MOD) % MOD;
nv2 = (MOD + 1) >> 1;
for (int i = 0; i <= n; ++i) {
C[i][0] = 1;
for (int j = 1; j <= i; ++j)
C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
}
}
int query(int k) {
if (MOD == 1) return 0;
static Mont a[N], b[N], a1[N], b1[N], res[N];
int t1 = n / k, t2 = n / k + 1,
c2 = n % k, c1 = k - c2;
Mont prd, nv;
prd = mpow(f[t1][1], c1);
nv = f[t1][1] == 1 ? 1 : f[t1][1] == 2 ? nv2 : MOD - nv2;
for (int i = 1; i <= t1; ++i)
a[i - 1] = Mont(f[t1][i]) * nv * fac[i - 1];
prd = prd * mpow(f[t2][1], c2);
nv = f[t2][1] == 1 ? 1 : f[t2][1] == 2 ? nv2 : MOD - nv2;
for (int i = 1; i <= t2; ++i)
b[i - 1] = Mont(f[t2][i]) * nv * fac[i - 1];
res[0] = a1[0] = b1[0] = 1;
for (int i = 1; i <= n - k; ++i) {
Mont x = Mont();
for (int j = 1; j <= min(i, t1 - 1); ++j)
x += a[j] * a1[i - j] * C[i - 1][j - 1];
Mont y = 0;
for (int j = 1; j <= min(i, t2 - 1); ++j)
y += b[j] * b1[i - j] * C[i - 1][j - 1];
res[i] = x * c1 + y * c2;
a1[i] = b1[i] = res[i];
for (int j = 1; j <= min(i, t1 - 1); ++j)
a1[i] -= a1[i - j] * a[j] * C[i][j];
for (int j = 1; j <= min(i, t2 - 1); ++j)
b1[i] -= b1[i - j] * b[j] * C[i][j];
}
Mont ans = 0;
for (int i = 0; i <= n - k; ++i)
ans += res[i] * C[i + k][i] * Mont(fac[k]);
ans *= prd;
return ans.get();
}
};
int dp[N], dp1[N];
int exGcd(int a, int b, int &x, int &y) {
if (!b) {
x = 1;
y = 0;
return a;
}
int ret = exGcd(b, a % b, y, x);
y -= a / b * x;
return ret;
}
int inv(int a, int p) {
int x, y;
exGcd(a, p, x, y);
if (x < 0)
x += p;
return x;
}
struct SolverManager : Solver {
ui M2, MO, i2, io;
Solver2 solver2;
SolverOdd solverOdd;
void setMOD(int MOD) {
Solver::setMOD(MOD);
fac[0] = 1;
for (int i = 1; i <= n; ++i)fac[i] = fac[i - 1] * (ull) i % MOD;
dp[0] = 1;
for (int i = 1; i <= n; ++i) {
copy(dp, dp + n + 1, dp1);
for (int j = 1; j <= n; ++j) {
sub(dp1[j], dp1[j - 1]);
}
for (int j = 0; j <= n; ++j) {
dp[j] = norm(MOD + norm(dp1[j] << 1) - dp[j]);
}
for (int j = i; j <= n; ++j) {
f[j][i] = dp[j - i];
}
}
M2 = 1, MO = MOD;
while (MO % 2 == 0) {
MO /= 2;
M2 *= 2;
}
solver2.setMOD(M2);
solverOdd.setMOD(MO);
i2 = inv(MO, M2) * (ull) MO % MOD;
io = inv(M2, MO) * (ull) M2 % MOD;
}
int query(int k) {
int r2 = solver2.query(k), ro = solverOdd.query(k);
return (r2 * (ull) i2 + ro * (ull) io) % MOD;
}
};
SolverManager solver;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n;
solver.setMOD(1000000007);
cout << solver.query(2) << '\n';
return 0;
}