Divisor Analysis - CSES

//Make CSP great again
#include <bits/stdc++.h>
#define TASK "TESTCODE"
using namespace std;
const int N = 1e6, mod = 1e9 + 7;
long long cnt[N + 1];
int n;
int Pow(int a, long long b)
{
    if (b == 0)
    {
        return 1;
    }
    int t = Pow(a, b/2);
    if (b % 2 == 0)
    {
        return (1LL * t * t) % mod;
    }
    else
    {
        return ((1LL * t * t) % mod * a) % mod;
    }
}
int Count(int i)
{
    return (1LL * (Pow(i, cnt[i] + 1) - 1) * Pow(i - 1, mod - 2)) % mod;
}
void read()
{
    cin >> n;
    for (int i = 1; i <= n; ++ i)
    {
        int x, k;
        cin >> x >> k;
        cnt[x] += k;
    }
}
void solve()
{
    int res1 = 1, res2 = 1, res3 = 1, divcnt = 1;
    for (int i = 2; i <= N; ++ i)
    {
        res1 = (1LL * res1 * (cnt[i] + 1)) % mod;
        res2 = (1LL * res2 * Count(i)) % mod;
        res3 = (1LL * Pow(res3, cnt[i] + 1) * Pow(Pow(i, cnt[i] * (cnt[i] + 1)/2), divcnt) ) % mod;
        divcnt = (1LL * divcnt * (cnt[i] + 1)) % (mod - 1);
    }
    cout << res1 << ' ' << res2 << ' ' << res3;
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    if (fopen(TASK".INP", "r"))
    {
        freopen(TASK".INP", "r", stdin);
        //freopen(TASK".OUT", "w", stdout);
    }
    int t = 1;
    bool typetest = false;
    if (typetest)
    {
        cin >> t;
    }
    for (int __ = 1; __ <= t; ++ __)
    {
        //cout << "Case " << __ <<": ";
        read();
        solve();
    }
}
;