From c7dc5357ee1f828e80a991c5851d70a4432839f7 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Mon, 9 Jan 2023 16:43:05 +0800
Subject: [PATCH] E - Positions in Permutations

https://codeforces.com/contest/285/submission/188561174
---
 Codeforces/285/E/E.cpp | 67 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 67 insertions(+)
 create mode 100644 Codeforces/285/E/E.cpp

diff --git a/Codeforces/285/E/E.cpp b/Codeforces/285/E/E.cpp
new file mode 100644
index 00000000..87145707
--- /dev/null
+++ b/Codeforces/285/E/E.cpp
@@ -0,0 +1,67 @@
+#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;
+}