SQRNUM.cpp

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const ll MOD = 1e9 + 7;

int minPrime[10000001];

ll binpow(ll a, ll b) {
    if (b == 0) return 1;
    ll t = binpow(a, b / 2);
    t = (t * t) % MOD;
    if (b % 2) return (t * a) % MOD;
    return t;
}

void solve() {
    int n; cin >> n;
    vector<int> a(n + 1);
    for (int i = 1; i <= n; i++) {
        int j = i;
        while (j != 1) {
            a[minPrime[j]]++;
            j /= minPrime[j];
        }
    }
    ll ans = 1;
    for (int i = 1; i <= n; i++) {
        ans *= binpow(i, a[i] - a[i] % 2);
        ans %= MOD;
    }
    cout << ans << '\n';
}

int main() {
    cin.tie(0)->sync_with_stdio(0);
    for (int i = 2; i <= 10000000; i++) {
        if (minPrime[i]) continue;
        for (int j = i; j <= 10000000; j += i) {
            if (!minPrime[j]) minPrime[j] = i;
        }
    }
    int T = 1; cin >> T;
    while (T--) solve();
}