#include<iostream>
#include<sstream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<string>
#include<vector>
#include<cmath>
#include<set>
#include<map>
#include<stack>
#include<queue>
#include<numeric>
#include<functional>
#include<complex>

using namespace std;
#define BET(a,b,c) ((a)<=(b)&&(b)<(c))
#define FOR(i,n) for(int i=0,i##_end=(int(n));i<i##_end;i++)
#define SZ(x) (int)(x.size())
#define ALL(x) (x).begin(),(x).end()
#define MP make_pair
#define FOR_EACH(it,v) for(__typeof(v.begin()) it=v.begin(),it_end=v.end() ; it != it_end ; it++)
typedef vector<int> VI;
typedef vector<VI> VVI;

int countFactor(int x, int f){
    int cnt = 0;
    while(x % f == 0){
        x /= f;
        cnt++;
    }
    return cnt;
}

int main()
{
    int q;
    cin>>q;
    FOR(_,q){
        int seed, N, K, B;
        scanf("%d%d%d%d",&seed,&N,&K,&B);
        vector<long long> 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) % 100000009 ;
        }
        vector<pair<int,int> > factors;
        for(int i=2;i<=36;i++){
            if(B % i == 0){
                int cnt = 0 ;
                while(B % i == 0){
                    B /= i;
                    cnt++;
                }
                factors.push_back(MP(i, cnt));
            }
        }
        int ans = 1<<28;
        for(auto p : factors){
            VI a;
            FOR(i,N+1) {
                a.push_back(countFactor(X[i], p.first));
            }
            sort(ALL(a));
            int sum = 0;
            FOR(i,K) sum += a[i];
            ans = min(ans, sum / p.second);
        }
        cout<<ans<<endl;
    }
    return 0;
}