P3807 【模板】卢卡斯定理/Lucas 定理

https://www.luogu.com.cn/record/79996740

Luogu/P3807/P3807.cpp

@@ -0,0 +1,48 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5;
+
+int t, n, m, p, fac[N], inv[N];
+
+inline int C(int n, int m, int p) {
+    if (m > n) return 0;
+    return 1ll * fac[n] * inv[m] % p * inv[n - m] % p;
+}
+
+int lucas(int n, int m, int p) {
+    if (!m) return 1;
+    return static_cast<long long>(C(n % p, m % p, p)) * lucas(n / p, m / p, p) % p;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> t;
+
+    while (t--) {
+        cin >> n >> m >> p;
+
+        fac[0] = 1;
+        for (int i = 1; i <= 100000; i++) {
+            fac[i] = 1ll * fac[i - 1] * i % p;
+        }
+
+        inv[0] = inv[1] = 1;
+        for (int i = 2; i <= 100000; i++) {
+            inv[i] = static_cast<long long>(p - (p / i)) * inv[p % i] % p;
+        }
+
+        for (int i = 2; i <= 100000; i++) {
+            inv[i] = static_cast<long long>(inv[i - 1]) * inv[i] % p;
+        }
+
+        cout << lucas(n + m, n, p) << endl;
+    }
+
+    return 0;
+}