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E - Positions in Permutations
https://codeforces.com/contest/285/submission/188561174
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Codeforces/285/E/E.cpp
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67
Codeforces/285/E/E.cpp
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#include <iostream>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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const int N = 1005;
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const int mod = 1e9 + 7;
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int n, m, fac[N], inv[N], fac_inv[N], f[N][N][2][2], g[N], ans;
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inline int C(int n, int m) {
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return static_cast<long long>(fac[n]) * fac_inv[m] % mod * fac_inv[n - m] % mod;
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}
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int main() {
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std::ios::sync_with_stdio(false);
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cin.tie(nullptr);
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fac[0] = 1;
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for (int i = 1; i < N; i++) {
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fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
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}
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inv[0] = inv[1] = 1;
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for (int i = 2; i < N; i++) {
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inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
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}
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fac_inv[0] = fac_inv[1] = 1;
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for (int i = 2; i < N; i++) {
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fac_inv[i] = static_cast<long long>(fac_inv[i - 1]) * inv[i] % mod;
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}
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cin >> n >> m;
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f[1][0][0][0] = f[1][1][0][1] = 1;
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for (int i = 2; i <= n; i++) {
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f[i][0][0][0] = 1;
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for (int j = 1; j <= i; j++) {
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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;
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f[i][j][0][1] = (static_cast<long long>(f[i - 1][j - 1][0][0]) + f[i - 1][j - 1][1][0]) % mod;
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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;
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f[i][j][1][1] = (static_cast<long long>(f[i - 1][j - 1][0][1]) + f[i - 1][j - 1][1][1]) % mod;
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}
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}
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f[n][0][0][0] = 1;
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for (int i = 1; i <= n; i++) {
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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;
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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;
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}
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for (int i = 0; i <= n; i++) {
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g[i] = (static_cast<long long>(f[n][i][0][0]) + f[n][i][1][0]) % mod * fac[n - i] % mod;
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}
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for (int i = m; i <= n; i++) {
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ans = (static_cast<long long>(ans) + (static_cast<long long>((i - m) & 1 ? -1 : 1) * C(i, m) * g[i] % mod + mod) % mod) % mod;
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}
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cout << ans << endl;
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return 0;
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}
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