#include <bits/stdc++.h>
using namespace std;
#define repl(i, l, r) for (ll i = (l); i < (r); i++)
#define rep(i, n) repl(i, 0, n)
#define CST(x) cout << fixed << setprecision(x)
using ll = long long;
const ll MOD = 100000009;
const ll r = 12345;
void solve() {
	ll a, n, k, b;
	cin >> a >> n >> k >> b;
	n++;
	vector<ll> vec(n);
	vec[0] = a;
	rep(i, n - 1) vec[i + 1] = 1 + (vec[i] * vec[i] + vec[i] * r) % MOD;
	map<ll, ll> m;
	ll B = b;
	repl(i, 2, (ll)sqrt(b) + 1) {
		while (B % i == 0) {
			m[i]++;
			B /= i;
		}
	}
	if (B != 1) m[B]++;
	ll ans = n * 40;
	for (auto p : m) {
		vector<int> cnt(n);
		rep(i, n) {
			ll v = vec[i];
			while (v % p.first == 0) {
				cnt[i]++;
				v /= p.first;
			}
		}
		sort(cnt.begin(), cnt.end());
		ll now = 0;
		rep(i, k) now += cnt[i];
		ans = min(ans, now / p.second);
	}
	cout << ans << endl;
	return;
}
int main() {
	cin.tie(0);
	cout.tie(0);
	ios::sync_with_stdio(false);

	int q;
	cin >> q;
	while (q--) solve();
	return 0;
}