#include #include #include #include #define repeat(i,n) for (int i = 0; (i) < (n); ++(i)) #define repeat_from(i,m,n) for (int i = (m); (i) < (n); ++(i)) typedef long long ll; using namespace std; vector sieve_of_eratosthenes(int n) { // enumerate primes in [2,n] with O(n log log n) vector is_prime(n+1, true); is_prime[0] = is_prime[1] = false; for (int i = 2; i*i <= n; ++i) if (is_prime[i]) for (int k = i+i; k <= n; k += i) is_prime[k] = false; vector primes; for (int i = 2; i <= n; ++i) if (is_prime[i]) primes.push_back(i); return primes; } vector factors(ll n, vector const & primes) { vector result; for (int p : primes) { if (n < p *(ll) p) break; while (n % p == 0) { result.push_back(p); n /= p; } } if (n != 1) result.push_back(n); return result; } ll powi(ll x, ll y, ll p) { // O(log y) assert (y >= 0); x = (x % p + p) % p; ll z = 1; for (ll i = 1; i <= y; i <<= 1) { if (y & i) z = z * x % p; x = x * x % p; } return z; } ll inv(ll x, ll p) { // p must be a prime, O(log p) assert ((x % p + p) % p != 0); return powi(x, p-2, p); } int main() { const vector primes = sieve_of_eratosthenes(sqrt(1e9) + 3); int t; cin >> t; while (t --) { ll n, m; cin >> n >> m; assert (0 <= n and n <= 1e9); assert (1 <= m and m <= 1e9); assert (m <= n + 1e5); vector ps = factors(m, primes); ll ans; if (ps.empty()) { ans = 0; } else if (ps.size() == 1) { ans = m - 1; repeat_from (i,n+1,m) { ans = ans * inv(i, m) % m; } } else { ans = 1; repeat_from (i,1,n+1) { ans = ans * (i+1) % m; if (ans == 0) break; } } cout << ans << endl; } return 0; }