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

using namespace std;
using ll = long long;

void solve(){
    ll s,n,k,b;
    cin>>s>>n>>k>>b;
    vector<ll> use;
    use.push_back(s);
    for(int i = 0;i<n;i++){
        ll x = use.back();
        ll nxt = 1 + (x*x+12345*x)%100000009;
        use.push_back(nxt);
    }
    vector<pair<ll,ll>> fac;
    ll now = b;
    for(int i = 2;i<=b;i++){
        if(now%i!=0) continue;
        int cnt = 0;
        while(now%i==0){
            now /= i;
            cnt++;
        }
        fac.push_back(make_pair(i,cnt));
    }
    ll ans = 1e9;
    for(int i = 0;i<fac.size();i++){
        vector<ll> all;
        for(int j = 0;j<use.size();j++){
            int cnt = 0;
            while(use[j]%fac[i].first==0){
                use[j] /= fac[i].first;
                cnt++;
            }
            all.push_back(cnt);
        }
        ll can = 0;
        sort(all.begin(),all.end());
        for(int j = 0;j<k;j++) can += all[j];
        //cout<<i<<" "<<can<<endl;
        ans = min(ans,can/fac[i].second);
    }
    cout<<ans<<endl;
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int t;
    cin>>t;
    while(t--){
        solve();
    }
}