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| #include <bits/stdc++.h>
using LL = long long;
const int N = 1e7 + 100;
int n, m, P, ans;
int fac[N], pr[N], cnt, imp[N], mp[N];
bool vis[N];
int qpow(int x, int y)
{
int res = 1;
for (; y; y >>= 1, x = LL(x) * x % P) if (y & 1) res = LL(res) * x % P;
return res;
}
void prev()
{
fac[0] = fac[1] = 1;
for (int i = 2; i < N; ++i) fac[i] = LL(fac[i - 1]) * i % P;
for (int i = 2; i < N; ++i)
{
if (!vis[i]) pr[++cnt] = i;
for (int j = 1; j <= cnt && LL(pr[j]) * i < N; ++j)
{
vis[pr[j] * i] = true;
if (i % pr[j] == 0) break;
}
}
for (int i = 1, j = 1, sum = 1, is = 1; i < N; ++i)
{
if (pr[j] == P) ++j;
if (j <= cnt && pr[j] <= i) sum = LL(pr[j++]) * sum % P, is = qpow(sum, P - 2);
imp[i] = is;
}
for (int i = 1, j = 1, sum = 1; i < N; ++i)
{
if (j <= cnt && pr[j] <= i) sum = LL(pr[j++] - 1) * sum % P;
mp[i] = sum;
}
}
int main()
{
int T;
scanf("%d %d", &T, &P);
prev();
while (T--)
{
scanf("%d %d", &n, &m);
if (n >= P && m < P) puts("0");
else
{
ans = LL(fac[n]) * imp[m] % P * mp[m] % P;
printf("%d\n", ans);
}
}
return 0;
}
|