#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#include <set>
#include <map>
#include <queue>
#include <iostream>
#include <sstream>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <cctype>
#include <cassert>
#include <limits>
#include <functional>
#define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i))
#define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i))
#if defined(_MSC_VER) || __cplusplus > 199711L
#define aut(r,v) auto r = (v)
#else
#define aut(r,v) __typeof(v) r = (v)
#endif
#define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it)
#define all(o) (o).begin(), (o).end()
#define pb(x) push_back(x)
#define mp(x,y) make_pair((x),(y))
#define mset(m,v) memset(m,v,sizeof(m))
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
using namespace std;
typedef vector<int> vi; typedef pair<int,int> pii; typedef vector<pair<int,int> > vpii; typedef long long ll;
template<typename T, typename U> inline void amin(T &x, U y) { if(y < x) x = y; }
template<typename T, typename U> inline void amax(T &x, U y) { if(x < y) x = y; }

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

int rec(const vi &X, map<pii,int> &add, int K, int B) {
	int N = X.size();
	if(B == 1) {
		int res = INF;
		each(i, add)
			amin(res, i->second / i->first.second);
		return res;
	}
	vpii fs;
	for(int b = B, p = 2; b != 1; ++ p) if(b % p == 0) {
		int q = 0;
		while(b % p == 0) ++ q, b /= p;
		fs.push_back(mp(p, q));
	}
	int res = INF;
	vpii v(N); vi nx;
	each(it, fs) {
		int p = it->first, q = it->second;
		rep(i, N)
			v[i] = mp(getv(X[i], p), X[i]);
		sort(all(v));
		int lastv = v[K-1].first;
		int i = 0;
		for(; v[i].first < lastv; ++ i)
			;
		nx.resize(K - i);
		rep(j, K - i) nx[j] = v[i + j].second;
		int remb = B;
		rep(i, q) remb /= p;

		rep(j, K) {
			each(jt, fs) if(j < i || jt == it)
				add[*jt] += getv(v[j].second, jt->first);
		}
		amin(res, rec(nx, add, K - i, remb));
		rep(j, K) {
			each(jt, fs) if(j < i || jt == it)
				add[*jt] -= getv(v[j].second, jt->first);
		}

		if(K == 0 || K == N) break;
	}
	return res;
}

unsigned xor128() {
	static unsigned x = 123456789, y = 362436069, z = 521288629, w = 88675123;
	unsigned t = x ^ (x << 11);
	x = y; y = z; z = w;
	return w = w ^ (w >> 19) ^ (t ^ (t >> 8));
}

int main() {
	int Q;
	cin >> Q;
	rep(ii, Q) {
		int seed, N, K, B;
		cin >> seed >> N >> K >> B;
//		seed=xor128()%100000009+1,N=10000,K=N/2,B=xor128()%35+2;
		vi X(N+1);
		X[0] = seed;
		rer(n, 1, N) X[n] = 1 + ((ll)X[n-1] * X[n-1] + X[n-1] * 12345LL) % 100000009;
		map<pii,int> add;
		int ans = rec(X, add, K, B);
		printf("%d\n", ans);
	}
	return 0;
}