#include <bits/stdc++.h>

#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define RFOR(i, a, b) for (ll i = (b)-1; i >= (a); i--)
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define rep1(i, n) for (ll i = 1; i <= (n); i++)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; i--)

#define pb push_back
#define mp make_pair
#define fst first
#define snd second
#define show(x) cout << #x << " = " << x << endl
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define pii pair<int, int>
#define vi vector<int>

using namespace std;
template <class S, class T>
ostream& operator<<(ostream& o, const pair<S, T>& p)
{
    return o << "(" << p.first << "," << p.second << ")";
}
template <class T>
ostream& operator<<(ostream& o, const vector<T>& vc)
{
    o << "sz = " << vc.size() << endl
      << "[";
    for (const T& v : vc)
        o << v << ",";
    o << "]";
    return o;
}
using ll = long long;
constexpr ll MOD = 1e8 + 9;
constexpr int INF = numeric_limits<int>::max() / 10;

int main()
{
    vector<int> prime{{2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31}};
    int Q;
    cin >> Q;
    rep(q, Q)
    {
        ll seed;
        cin >> seed;
        int n, k, b;
        cin >> n >> k >> b;
        vector<pii> pf;
        for (int p : prime) {
            int n = 0;
            while (b % p == 0) {
                b /= p;
                n++;
            }
            if (n > 0) {
                pf.pb(mp(p, n));
            }
        }

        int mini = INF;
        for (const auto& p : pf) {
            ll x = seed;
            vector<int> ind(n + 1);
            for (int i = 0; i <= n; i++) {
                ll num = x;
                ll n = 0;
                while (num % p.first == 0) {
                    n++;
                    num /= p.first;
                }
                ind[i] = n;
                x = 1 + ((x * x) % MOD + (x * 12345LL) % MOD) % MOD;
            }
            sort(ind.begin(), ind.end());
            int sum = 0;
            for (int i = 0; i < k; i++) {
                sum += ind[i];
            }
            mini = min(mini, sum / p.second);
        }
        cout << mini << endl;
    }
    return 0;
}