P2155 [SDOI2008] 沙拉公主的困惑

https://www.luogu.com.cn/record/96680376

Luogu/P2155/P2155.cpp

@@ -0,0 +1,70 @@
+#include <iostream>
+#include <algorithm>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e7 + 5;
+
+int t, mod, p, primes[N], fac[N], fac_phi[N];
+bool not_prime[N];
+
+int binpow(int a, int b) {
+    int res = 1;
+
+    while (b) {
+        if (b & 1) res = static_cast<long long>(res) * a % mod;
+        a = static_cast<long long>(a) * a % mod;
+        b >>= 1;
+    }
+
+    return res;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> t >> mod;
+
+    for (int i = 2; i < N; i++) {
+        if (!not_prime[i]) primes[++p] = i;
+
+        for (int j = 1; j <= p && i * primes[j] < N; j++) {
+            not_prime[i * primes[j]] = true;
+
+            if (i % primes[j] == 0) break;
+        }
+    }
+
+    fac[0] = 1;
+
+    for (int i = 1; i < N; i++) {
+        if (i % mod) {
+            fac[i] = static_cast<long long>(fac[i - 1]) * i % mod;
+        } else {
+            fac[i] = fac[i - 1];
+        }
+    }
+
+    fac_phi[1] = 1;
+
+    for (int i = 2; i < N; i++) {
+        if (not_prime[i]) {
+            fac_phi[i] = static_cast<long long>(fac_phi[i - 1]) * i % mod;
+        } else {
+            fac_phi[i] = static_cast<long long>(fac_phi[i - 1]) * (i - 1) % mod;
+        }
+    }
+
+    while (t--) {
+        int n, m;
+
+        cin >> n >> m;
+
+        cout << (n / mod > m / mod ? 0 : static_cast<long long>(fac[n]) * fac_phi[m] % mod * binpow(fac[m], mod - 2) % mod) << endl;
+    }
+
+    return 0;
+}