P5431 【模板】乘法逆元 2

https://www.luogu.com.cn/record/89461048

Luogu/P5431/P5431.cpp

@@ -0,0 +1,53 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 5e6 + 5;
+
+int n, p, _k, k, a[N], b[N], s[N], ans;
+
+int binpow(int a, int b) {
+    int res = 1;
+
+    while (b) {
+        if (b & 1) res = static_cast<long long>(res) * a % p;
+        a = static_cast<long long>(a) * a % p;
+        b >>= 1;
+    }
+
+    return res;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> p >> _k;
+
+    s[0] = 1;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+
+        s[i] = static_cast<long long>(s[i - 1]) * a[i] % p;
+    }
+
+    b[n + 1] = binpow(s[n], p - 2);
+
+    for (int i = n; i; i--) {
+        b[i] = static_cast<long long>(b[i + 1]) * a[i] % p;
+    }
+
+    k = _k;
+
+    for (int i = 1; i <= n; i++) {
+        ans = (ans + static_cast<long long>(s[i - 1]) * b[i + 1] % p * k) % p;
+        k = static_cast<long long>(k) * _k % p;
+    }
+
+    cout << ans << endl;
+
+    return 0;
+}