#include <iostream>
#include <map>
#include <queue>

using namespace std;

const int INF = 1000000;

int Q, seed, N, K, B;
long long X[10001];
map<int, int> divisors[37];

void setX() {
	X[0] = seed;
	for (int i = 1; i <= N; i++) {
		X[i] = 1 + (X[i - 1] * X[i - 1] + X[i - 1] * 12345) % 100000009;
	}
}

int num(int divisor) {
	priority_queue<int> P;
	for (int i = 0; i <= N; i++) {
		int cnt = 0;
		int n = X[i];
		while (n % divisor == 0) {
			cnt++;
			n /= divisor;
		}
		P.push(-cnt);
	}
	int res = 0;
	for (int i = 0; i < K; i++) {
		res -= P.top();
		P.pop();
	}
	return res;
}

int main() {
	for (int i = 2; i <= 36; i++) {
		int n = i;
		for (int d = 2; d <= i; d++) {
			int cnt = 0;
			while (n % d == 0) {
				cnt++;
				n /= d;
			}
			if (cnt > 0) {
				divisors[i][d] = cnt;
			}
		}
	}
	cin >> Q;
	for (int i = 0; i < Q; i++) {
		cin >> seed >> N >> K >> B;
		setX();
		int mi = INF;
		for (const auto& itr : divisors[B]) {
			mi = min(mi, num(itr.first) / itr.second);
		}
		cout << mi << endl;
	}
	return 0;
}