#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(ll i=0;i<n;i++)
#define repl(i,l,r) for(ll i=(l);i<(r);i++)
#define per(i,n) for(ll i=n-1;i>=0;i--)
#define perl(i,r,l) for(ll i=r-1;i>=l;i--)
#define fi first
#define se second
#define pb push_back
#define ins insert
#define pqueue(x) priority_queue<x,vector<x>,greater<x>>
#define all(x) (x).begin(),(x).end()
#define CST(x) cout<<fixed<<setprecision(x)
#define vtpl(x,y,z) vector<tuple<x,y,z>>
#define rev(x) reverse(x);
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vector<ll>>;
using pl=pair<ll,ll>;
using vpl=vector<pl>;
using vvpl=vector<vpl>;
const ll MOD=1000000007;
const ll MOD9=998244353;
const int inf=1e9+10;
const ll INF=4e18;
const ll dy[8]={1,0,-1,0,1,1,-1,-1};
const ll dx[8]={0,-1,0,1,1,-1,1,-1};
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template<class T> inline bool chmax(T& a, T b) {
    if (a <= b) {
        a = b;
        return true;
    }
    return false;
}
ll mod=100000009;
ll prime[11]={2,3,5,7,11,13,17,19,23,29,31};
int main(){
    ll q;cin >> q;
    while(q--){
        ll seed,n,k,b;cin >> seed >> n >> k >> b;
        vl v(n+1);v[0]=seed;
        rep(i,n)v[i+1]=1+(v[i]*v[i]+v[i]*12345)%mod;
        vpl z;
        rep(i,11){
            ll cnt=0;
            while(b%prime[i]==0){
                cnt++;b/=prime[i];
            }
            if(cnt)z.pb({prime[i],cnt});
        }
        ll ans=inf;
        for(auto p:z){
            vector<ll> num(n+1);
            rep(i,n+1){
                while(v[i]%p.fi==0){
                    v[i]/=p.fi;num[i]++;
                }
            }
            //for(auto x:num)cout << x <<" " ;cout << endl;
            sort(all(num));
            ll ret=0;
            rep(i,k)ret+=num[i];
            ret/=p.se;
            chmin(ans,ret);
        }
        cout << ans <<endl;
    }
}