#include "bits/stdc++.h"
using namespace std;
#define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i))
#define rep(i,j) FOR(i,0,j)
#define each(x,y) for(auto &(x):(y))
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define debug(x) cout<<#x<<": "<<(x)<<endl
#define smax(x,y) (x)=max((x),(y))
#define smin(x,y) (x)=min((x),(y))
#define MEM(x,y) memset((x),(y),sizeof (x))
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vll;

template<class Val>
map<Val, int> factorize(Val n){
    map<Val, int> res;
    for(Val i=2; (long long)i*i<=n; ++i){
        while(n%i==0){
            n /= i;
            ++res[i];
        }
    }
    if(n!=1) ++res[n];
    return res;
}

const int MOD = (int)1e8 + 9, MAXB = 36, MAXN = 10001;
ll X[MAXN];
int seed, N, K, B, cnt[MAXN];

void genX(){
    X[0] = seed;
    rep(i, N){
        X[i + 1] = 1 + (X[i] * X[i] + X[i] * 12345) % MOD;
    }
    N++;
}

void solve(){
    genX();
    int ans = INT_MAX;
    auto fact = factorize(B);
    each(fa, fact){
        int p, q, r = 0;
        tie(p, q) = fa;
        rep(i, N){
            int x = (int)X[i], y = 0;
            while(x%p == 0){
                y++;
                x /= p;
            }
            cnt[i] = y;
        }
        sort(cnt, cnt + N);
        rep(i, K)r += cnt[i];
        smin(ans, r / q);
    }
    cout << ans << endl;
}

int main(){
    int Q;
    cin >> Q;
    while(Q--){
        cin >> seed >> N >> K >> B;
        solve();
    }
}