#line 2 "header.hpp"

//%snippet.set('header')%
//%snippet.fold()%
#ifndef HEADER_H
#define HEADER_H

// template version 2.0
using namespace std;
#include <bits/stdc++.h>

// varibable settings
const long long INF = 1e18;
template <class T> constexpr T inf = numeric_limits<T>::max() / 2.1;

#define _overload3(_1, _2, _3, name, ...) name
#define _rep(i, n) repi(i, 0, n)
#define repi(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define rep(...) _overload3(__VA_ARGS__, repi, _rep, )(__VA_ARGS__)
#define _rrep(i, n) rrepi(i, 0, n)
#define rrepi(i, a, b) for (ll i = (ll)((b)-1); i >= (ll)(a); --i)
#define r_rep(...) _overload3(__VA_ARGS__, rrepi, _rrep, )(__VA_ARGS__)
#define each(i, a) for (auto &&i : a)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((int)(x).size())
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define mt(...) make_tuple(__VA_ARGS__)
#define ub upper_bound
#define lb lower_bound
#define lpos(A, x) (lower_bound(all(A), x) - A.begin())
#define upos(A, x) (upper_bound(all(A), x) - A.begin())
template <class T> inline void chmax(T &a, const T &b) { if ((a) < (b)) (a) = (b); }
template <class T> inline void chmin(T &a, const T &b) { if ((a) > (b)) (a) = (b); }
template <typename X, typename T> auto make_table(X x, T a) { return vector<T>(x, a); }
template <typename X, typename Y, typename Z, typename... Zs> auto make_table(X x, Y y, Z z, Zs... zs) { auto cont = make_table(y, z, zs...); return vector<decltype(cont)>(x, cont); }

#define cdiv(a, b) (((a) + (b)-1) / (b))
#define is_in(x, a, b) ((a) <= (x) && (x) < (b))
#define uni(x) sort(all(x)); x.erase(unique(all(x)), x.end())
#define slice(l, r) substr(l, r - l)

typedef long long ll;
typedef long double ld;
using vl = vector<ll>;
using vvl = vector<vl>;
using pll = pair<ll, ll>;

template <typename T>
using PQ = priority_queue<T, vector<T>, greater<T>>;
void check_input() { assert(cin.eof() == 0); int tmp; cin >> tmp; assert(cin.eof() == 1); }

#if defined(PCM) || defined(LOCAL)
#else
#define dump(...) ;
#define dump_1d(...) ;
#define dump_2d(...) ;
#define cerrendl ;
#endif

#endif /* HEADER_H */
//%snippet.end()%
#line 2 "solve.cpp"
template<class T=ll> using vec = vector<T>;
struct Fast { Fast() { std::cin.tie(0); ios::sync_with_stdio(false); } } fast;

// snippet:sieve {{{
struct Sieve {/*{{{*/
    // エラトステネスのふるい O(NloglogN)
    ll n;                              // n: max number for defined f and primes
    vector<ll> f;                      // [-1, 2, 3, 2, 5, 2, 7, 2, 3, ....]
    vector<ll> primes;                 // [2, 3, 5, .......]
    Sieve(ll n = 1) : n(n), f(n + 1) { /*{{{*/
        f[0] = f[1] = -1;
        for (ll i = 2; i <= n; ++i) {
            if (f[i]) continue;
            primes.push_back(i);
            f[i] = i;
            for (ll j = i * i; j <= n; j += i) {
                if (!f[j]) f[j] = i;
            }
        }
    } /*}}}*/
    bool is_prime(ll x) {
        if (x <= n) return f[x] == x; 
        return sz(factor_list(x)) == 1;
    }

    vector<ll> factor_list(ll x) { /*{{{*/
        assert(x <= n*n); // これが満たされないと正しく計算されない可能性がある。

        vector<ll> res;
        if (x <= n) {
            while (x != 1) {
                res.push_back(f[x]);
                x /= f[x];
            }
        }
        else {
            for (ll i = 0; primes[i] * primes[i] <= x; i++) {
                while (x % primes[i] == 0) {
                    res.pb(primes[i]);
                    x /= primes[i];
                }
            }
            if (x != 1) res.pb(x);
        }

        return res;  // [2, 3, 3, 5, 5, 5.....]
    }                /*}}}*/

    vector<pair<ll, ll>> prime_factor(ll x) { /*{{{*/
        // just change fl vector to map form
        vector<ll> fl = factor_list(x);
        if (fl.size() == 0) return {};
        vector<pair<ll, ll>> res = {mp(fl[0], 0)};
        for (ll p : fl) {
            if (res.back().first == p) {
                res.back().second++;
            } else {
                res.emplace_back(p, 1);
            }
        }
        return res;  // [(2,1), (3,2), (5,3), .....]
    }                /*}}}*/
};/*}}}*/
Sieve sv(1e6);
// How to use
// sv.primes            // 素数のリスト
// sv.prime_factor(x);  // 素因数分解
// snippet:sieve }}}

int solve() {
    ll Q;cin>>Q;
    const ll mod = 100'000'009;
    rep(q, Q){
        ll x0;cin>>x0;
        ll n,k,b;cin>>n>>k>>b;
        auto ps = sv.prime_factor(b);
        vl x(n+1);
        x[0] = x0;
        rep(i, 1, n+1){ x[i] = 1 + (x[i-1]*x[i-1]%mod + x[i-1]*12345%mod) % mod; }
        
        ll minimum = INF;
        each(el, ps){
            auto [p, c] = el;
            vl xx(x);
            auto count = [&](ll y) -> ll{ll res = 0; while(y%p==0){ y /= p; res++; } return res;};
            sort(all(xx), [&](auto &l, auto &r){return count(l) < count(r);});
            ll sc = 0;
            rep(i, k) sc += count(xx[i]);
            chmin(minimum, sc/c);
        }
        cout << minimum << endl;
    }
    return 0; 
}


int main(){/*{{{*/
    solve();
    return 0;
}/*}}}*/