#line 2 "header.hpp" //%snippet.set('header')% //%snippet.fold()% #ifndef HEADER_H #define HEADER_H // template version 2.0 using namespace std; #include // varibable settings const long long INF = 1e18; template constexpr T inf = numeric_limits::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 inline void chmax(T &a, const T &b) { if ((a) < (b)) (a) = (b); } template inline void chmin(T &a, const T &b) { if ((a) > (b)) (a) = (b); } template auto make_table(X x, T a) { return vector(x, a); } template auto make_table(X x, Y y, Z z, Zs... zs) { auto cont = make_table(y, z, zs...); return vector(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; using vvl = vector; using pll = pair; template using PQ = priority_queue, greater>; 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 using vec = vector; 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 f; // [-1, 2, 3, 2, 5, 2, 7, 2, 3, ....] vector 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 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 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> prime_factor(ll x) { /*{{{*/ // just change fl vector to map form vector fl = factor_list(x); if (fl.size() == 0) return {}; vector> 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; }/*}}}*/