P4071 [SDOI2016]排列计数

https://www.luogu.com.cn/record/80167680

Luogu/P4071/P4071.cpp

@@ -0,0 +1,49 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e6 + 5;
+const int mod = 1e9 + 7;
+
+int t, n, m, fac[N], inv[N], fac_inv[N], d[N];
+
+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;
+    }
+
+    d[2] = 1;
+    for (int i = 3; i < N; i++) {
+        d[i] = static_cast<long long>(i - 1) * (d[i - 1] + d[i - 2]) % mod;
+    }
+
+    cin >> t;
+
+    while (t--) {
+        cin >> n >> m;
+
+        cout << (n == m ? 1 : static_cast<long long>(d[n - m]) * C(n, m) % mod) << endl;
+    }
+
+    return 0;
+}