#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
using namespace std;
typedef long long ll;
typedef unsigned int ui;
const ll mod = (ll)(1e+8) + 9;
const ll INF = (ll)1000000007 * 1000000007;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef long double ld;
typedef complex<ld> Point;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ll, ll> LP;
typedef pair<ld, ld> LDP;
bool isp[37];
vector<int> p;
void init1() {
	fill(isp + 2, isp + 37, true);
	Rep(i, 2, 37) {
		if (!isp[i])continue;
		p.push_back(i);
		for (int j = 2 * i; j < 37; j += i) {
			isp[j] = false;
		}
	}
}
int main() {
	init1();
	int q; cin >> q;
	rep(aa, q) {
		ll s; int n, k; ll b;
		cin >> s >> n >> k >> b;
		int c[37] = {};
		vector<int> v[37];
		vector<int>d;
		rep1(i, b) {
			if (isp[i] && b % i == 0) {
				d.push_back(i);
				ll cop = b;
				while (cop%i == 0) {
					c[i]++; cop /= i;
				}
			}
		}
		rep(i, n + 1) {
			//cout << s << endl;
			rep(j, (int)d.size()) {
				int cnt = 0;
				ll cop = s;
				while (cop%d[j] == 0) {
					cnt++; cop /= d[j];
				}
				v[d[j]].push_back(cnt);
				//if (d[j] == 3)cout << cnt << endl;
			}
			s = 1 + (s*s + s * 12345) % mod;
		}
		ll mi = INF;
		rep(j, (int)d.size()){
			ll sum = 0;
			sort(v[d[j]].begin(), v[d[j]].end());
			rep(i, k) {
				sum += v[d[j]][i];
			}
			//cout << d[j] << " " << sum << endl;
			mi = min(mi, sum / c[d[j]]);
	    }
		cout << mi << endl;
	}
	return 0;
}