#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>

typedef long long ll;

typedef std::pair<int,int> P;

const ll MOD = 100000009ll;

int main(){
    int Q;
    scanf("%d", &Q);

    for(int _=0;_<Q;_++){
        ll seed, B;
        int N, K;
        
        scanf("%lld %d %d %lld", &seed, &N, &K, &B);
    
        std::vector<ll> v(N+1);
        v[0] = seed;
        for(int i=1;i<=N;i++){
            v[i] = 1 + (v[i-1]*v[i-1]%MOD + v[i-1]*12345%MOD) % MOD;
        }

        std::vector<P> fs;
        for(int i=2;i*i<=B;i++){
            if(B % i == 0){
                int t = 0;
                while(B % i == 0){t += 1; B /= i;}

                fs.push_back(std::make_pair(i, t));
            }
        }
        if(B > 1){fs.push_back(std::make_pair(B, 1));}

        // for(auto f : fs){
        //     printf("%d %d\n", f.first, f.second);
        // }

        std::vector<int> v2(N+1);
        int res = 1001001001;
        for(auto f : fs){
            int p = f.first, q = f.second;
            for(int i=0;i<N+1;i++){
                ll x = v[i];
                int t = 0;
                while(x % p == 0){t += 1; x /= p;}

                v2[i] = t;
            }

            std::sort(v2.begin(), v2.end());

            int sum = 0;
            for(int i=0;i<K;i++){
                sum += v2[i];
            }

            res = std::min(res, sum/q);
        }

        printf("%d\n", res);
    }
}