#include <bits/stdc++.h>
#define For(i, a, b) for(int (i)=(int)(a); (i)<(int)(b); ++(i))
#define rFor(i, a, b) for(int (i)=(int)(a)-1; (i)>=(int)(b); --(i))
#define rep(i, n) For((i), 0, (n))
#define rrep(i, n) rFor((i), (n), 0)
#define fi first
#define se second
using namespace std;
typedef long long lint;
typedef unsigned long long ulint;
typedef pair<int, int> pii;
typedef pair<lint, lint> pll;
template<class T> bool chmax(T &a, const T &b){if(a<b){a=b; return true;} return false;}
template<class T> bool chmin(T &a, const T &b){if(a>b){a=b; return true;} return false;}
template<class T> T div_floor(T a, T b){
    if(b < 0) a *= -1, b *= -1;
    return a>=0 ? a/b : (a+1)/b-1;
}
template<class T> T div_ceil(T a, T b){
    if(b < 0) a *= -1, b *= -1;
    return a>0 ? (a-1)/b+1 : a/b;
}

constexpr lint mod = 1e8+9;
constexpr lint INF = mod * mod;
constexpr int MAX = 10010;

int n, K, b, cnt[MAX];
lint x[MAX];

int f(int p, int a){
    rep(i, n+1){
        cnt[i] = 0;
        while(x[i]%p == 0){
            ++cnt[i];
            x[i] /= p;
        }
    }
    sort(cnt, cnt+n+1);
    return accumulate(cnt, cnt+K, 0) / a;
}

void solve(){
    int ans = mod;
    for(int p=2; p*p<=b; ++p)if(b%p == 0){
        int a = 0;
        while(b%p == 0){
            ++a;
            b /= p;
        }
        chmin(ans, f(p, a));
    }
    if(b > 1) chmin(ans, f(b, 1));
    printf("%d\n", ans);
}

int main(){
    int q;
    scanf("%d", &q);
    rep(qq, q){
        scanf("%lld%d%d%d", &x[0], &n, &K, &b);
        For(i, 1, n+1){
            x[i] = 1 + (x[i-1]*x[i-1] + x[i-1]*12345) % mod;
        }
        solve();
    }
}