#include <algorithm>
#include <iostream>
#include <cstdio>
#include <map>
#include <numeric>
#include <cmath>
#include <set>
#include <sstream>
#include <string>
#include <vector>
#include <queue>
#include <complex>
#include <string.h>
#include <unordered_set>
#include <unordered_map>
using namespace std;

#define endl '\n'
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define uniq(v) (v).erase(unique((v).begin(), (v).end()), (v).end())

typedef long long ll;
typedef pair<int, int> P;
typedef unsigned int uint;
typedef unsigned long long ull;
struct pairhash {
public:
    template<typename T, typename U>
    size_t operator()(const pair<T, U> &x) const {
	size_t seed = hash<T>()(x.first);
	return hash<U>()(x.second) + 0x9e3779b9 + (seed<<6) + (seed>>2);
    }
};

const int inf = 1000000009;
const ll mod = (ll)1e8 + 9;

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

int calc(ll num, int k) {
    int res = 0;
    while (num % k == 0) {
	res++;
	num /= k;
    }
    return res;
}

int solve(ll seed, int n, int k, int b) {
    ll x[n+1];
    x[0] = seed;
    for (int i = 1; i <= n; i++) {
	x[i] = 1 + (x[i-1] * x[i-1] + x[i-1] * 12345) % mod;
    }
    map<int, int> fact = prime_factor(b);

    int res = inf;
    for (auto& p : fact) {
	vector<int> t(n+1);
	for (int i = 0; i <= n; i++) {
	    t[i] = calc(x[i], p.first);
	}
	sort(all(t));
	int sum = 0;
	for (int i = 0; i < k; i++)
	    sum += t[i];
	res = min(res, sum / p.second);
    }
    return res;
}

int main() {
    int q;
    scanf("%d", &q);
    for (int i = 0; i < q; i++) {
	ll seed;
	int n, k, b;
	scanf("%lld%d%d%d", &seed, &n, &k, &b);
	printf("%d\n", solve(seed, n, k, b));
    }
}