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E - Positions in Permutations

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https://codeforces.com/contest/285/submission/188561174
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Baoshuo Ren 2023-01-09 16:43:05 +08:00
parent 4edce25d94
commit c7dc5357ee
Signed by: baoshuo
GPG Key ID: 00CB9680AB29F51A
1 changed files with 67 additions and 0 deletions
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Codeforces/285/E/E.cpp Normal file
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#include <iostream>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 1005;
const int mod = 1e9 + 7;
int n, m, fac[N], inv[N], fac_inv[N], f[N][N][2][2], g[N], ans;
inline int C(int n, int m) {
return static_cast<long long>(fac[n]) * fac_inv[m] % mod * fac_inv[n - m] % mod;
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
fac[0] = 1;
for (int i = 1; i < N; i++) {
fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
}
inv[0] = inv[1] = 1;
for (int i = 2; i < N; i++) {
inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
}
fac_inv[0] = fac_inv[1] = 1;
for (int i = 2; i < N; i++) {
fac_inv[i] = static_cast<long long>(fac_inv[i - 1]) * inv[i] % mod;
}
cin >> n >> m;
f[1][0][0][0] = f[1][1][0][1] = 1;
for (int i = 2; i <= n; i++) {
f[i][0][0][0] = 1;
for (int j = 1; j <= i; j++) {
f[i][j][0][0] = (static_cast<long long>(f[i - 1][j - 1][0][0]) + f[i - 1][j][0][0] + f[i - 1][j][1][0]) % mod;
f[i][j][0][1] = (static_cast<long long>(f[i - 1][j - 1][0][0]) + f[i - 1][j - 1][1][0]) % mod;
f[i][j][1][0] = (static_cast<long long>(f[i - 1][j - 1][0][1]) + f[i - 1][j][1][1] + f[i - 1][j][0][1]) % mod;
f[i][j][1][1] = (static_cast<long long>(f[i - 1][j - 1][0][1]) + f[i - 1][j - 1][1][1]) % mod;
}
}
f[n][0][0][0] = 1;
for (int i = 1; i <= n; i++) {
f[n][i][0][0] = (static_cast<long long>(f[n - 1][i - 1][0][0]) + f[n - 1][i][0][0] + f[n - 1][i][1][0]) % mod;
f[n][i][1][0] = (static_cast<long long>(f[n - 1][i - 1][0][1]) + f[n - 1][i][0][1] + f[n - 1][i][1][1]) % mod;
}
for (int i = 0; i <= n; i++) {
g[i] = (static_cast<long long>(f[n][i][0][0]) + f[n][i][1][0]) % mod * fac[n - i] % mod;
}
for (int i = m; i <= n; i++) {
ans = (static_cast<long long>(ans) + (static_cast<long long>((i - m) & 1 ? -1 : 1) * C(i, m) * g[i] % mod + mod) % mod) % mod;
}
cout << ans << endl;
return 0;
}