#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 main() {
	int Q;
	cin >> Q;
	rep(ii, Q) {
		int seed, N, K, B;
		cin >> seed >> N >> K >> B;
		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;
		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 ans = INF;
		vi v(N+1); vi nx;
		each(it, fs) {
			int p = it->first, q = it->second;
			rep(i, N+1)
				v[i] = getv(X[i], p);
			sort(all(v));
			amin(ans, accumulate(v.begin(), v.begin() + K, 0) / q);
		}
		printf("%d\n", ans);
	}
	return 0;
}