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OI-codes/Luogu/P3807/P3807.cpp

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#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;
}