#include <bits/stdc++.h>
using namespace std;
#define rep(i, a) for (int i = 0; i < (a); i++)
#define rep2(i, a, b) for (int i = (a); i < (b); i++)
#define repr(i, a) for (int i = (a) - 1; i >= 0; i--)
#define repr2(i, a, b) for (int i = (b) - 1; i >= (a); i--)
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
typedef long long ll;

map<long long, long long> primeFactors(long long n) {
	map<long long, long long> ret;
	for (long long i = 2; i * i <= n; i++)
		while (n % i == 0) ret[i]++, n /= i;
	if (n != 1) ret[n]++;
	return ret;
}

int countP(int x, int p) {
	int ret = 0;
	while (x % p == 0) ret++, x /= p;
	return ret;
}

int fac;
bool comp(int a, int b) {
	return countP(a, fac) < countP(b, fac);
}

void solve() {
	int seed, n, K, B;
	cin >> seed >> n >> K >> B;
	n++;
	vector<ll> X(n);
	const ll mod = 100000009;
	X[0] = seed;
	for (int i = 1; i < n; i++)
		X[i] = 1 + (X[i - 1] * X[i - 1] + X[i - 1] * 12345) % mod;

	auto pf = primeFactors(B);

	int ans = 1e9;
	for (auto kv : pf) {
		fac = kv.first;
		sort(X.begin(), X.end(), comp);
		int cand = 1e9;
		for (auto kv2 : pf) {
			int num = 0;
			rep(i, K) num += countP(X[i], kv2.first);
			chmin(cand, num / kv2.second);
		}
		chmin(ans, cand);
	}
	cout << ans << endl;
}

int main() {
	int q;
	cin >> q;
	rep(i, q) solve();
	return 0;
}