#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" using namespace std; #include #line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp" namespace noya2 { template ostream &operator<<(ostream &os, const pair &p){ os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v){ int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v){ for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u){ cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u){ cout << t; if (sizeof...(u)) cout << sep; out(u...); } template void out(const vector> &vv){ int s = (int)vv.size(); for (int i = 0; i < s; i++) out(vv[i]); } struct IoSetup { IoSetup(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetup_noya2; } // namespace noya2 #line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp" namespace noya2{ const int iinf = 1'000'000'007; const long long linf = 2'000'000'000'000'000'000LL; const long long mod998 = 998244353; const long long mod107 = 1000000007; const long double pi = 3.14159265358979323; const vector dx = {0,1,0,-1,1,1,-1,-1}; const vector dy = {1,0,-1,0,1,-1,-1,1}; const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string alp = "abcdefghijklmnopqrstuvwxyz"; const string NUM = "0123456789"; void yes(){ cout << "Yes\n"; } void no(){ cout << "No\n"; } void YES(){ cout << "YES\n"; } void NO(){ cout << "NO\n"; } void yn(bool t){ t ? yes() : no(); } void YN(bool t){ t ? YES() : NO(); } } // namespace noya2 #line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp" namespace noya2{ unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){ if (a == 0 || b == 0) return a + b; int n = __builtin_ctzll(a); a >>= n; int m = __builtin_ctzll(b); b >>= m; while (a != b) { int mm = __builtin_ctzll(a - b); bool f = a > b; unsigned long long c = f ? a : b; b = f ? b : a; a = (c - b) >> mm; } return a << min(n, m); } template T gcd_fast(T a, T b){ return static_cast(inner_binary_gcd(abs(a),abs(b))); } long long sqrt_fast(long long n) { if (n <= 0) return 0; long long x = sqrt(n); while ((x + 1) * (x + 1) <= n) x++; while (x * x > n) x--; return x; } template T floor_div(const T n, const T d) { assert(d != 0); return n / d - static_cast((n ^ d) < 0 && n % d != 0); } template T ceil_div(const T n, const T d) { assert(d != 0); return n / d + static_cast((n ^ d) >= 0 && n % d != 0); } template void uniq(vector &v){ sort(v.begin(),v.end()); v.erase(unique(v.begin(),v.end()),v.end()); } template inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline bool range(T l, T x, T r){ return l <= x && x < r; } } // namespace noya2 #line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define repp(i,m,n) for (int i = (m); i < (int)(n); i++) #define reb(i,n) for (int i = (int)(n-1); i >= 0; i--) #define all(v) (v).begin(),(v).end() using ll = long long; using ld = long double; using uint = unsigned int; using ull = unsigned long long; using pii = pair; using pll = pair; using pil = pair; using pli = pair; namespace noya2{ /* ~ (. _________ . /) */ } using namespace noya2; #line 2 "c.cpp" #line 2 "/Users/noya2/Desktop/Noya2_library/math/sieve.hpp" #line 4 "/Users/noya2/Desktop/Noya2_library/math/sieve.hpp" namespace noya2{ struct Sieve { vector primes, factor, mu; Sieve (int N = 1024){ build(N); } void request(int N){ int len = n_max(); if (len >= N) return ; while (len < N) len <<= 1; build(len); } int n_max(){ return factor.size()-1; } private: void build (int N){ primes.clear(); factor.resize(N+1); fill(factor.begin(),factor.end(),0); mu.resize(N+1); fill(mu.begin(),mu.end(),1); for(int n = 2; n <= N; n++) { if (factor[n] == 0){ primes.push_back(n); factor[n] = n; mu[n] = -1; } for (int p : primes){ if(n * p > N || p > factor[n]) break; factor[n * p] = p; mu[n * p] = p == factor[n] ? 0 : -mu[n]; } } } } sieve; int mobius_sieve(int n){ assert(1 <= n && n <= sieve.n_max()); return sieve.mu[n]; } bool is_prime_sieve(int n){ if (n <= 2) return n == 2; assert(n <= sieve.n_max()); return sieve.factor[n] == n; } vector> prime_factorization_sieve(int n){ assert(1 <= n && n <= sieve.n_max()); vector facts; while (n > 1){ int p = sieve.factor[n]; facts.push_back(p); n /= p; } vector> pes; int siz = facts.size(); for (int l = 0, r = 0; l < siz; l = r){ while (r < siz && facts[r] == facts[l]) r++; pes.emplace_back(facts[l],r-l); } return pes; } vector divisor_enumeration_sieve(int n){ auto pes = prime_factorization_sieve(n); vector divs = {1}; for (auto [p, e] : pes){ vector nxt; nxt.reserve(divs.size() * (e+1)); for (auto x : divs){ for (int tt = 0; tt <= e; tt++){ nxt.push_back(x); x *= p; } } swap(divs,nxt); } return divs; } } // namespace noya2 #line 4 "c.cpp" const int mx = 3001100; void solve(){ int t; in(t); vector rui(mx+1); rep(i,mx){ rui[i+1] = rui[i] + (is_prime_sieve(i) ? 1 : 0); } while (t--){ int n; in(n); if (is_prime_sieve(n)){ out("P"); continue; } int cnt = n-2; cnt -= rui[n+1] - rui[n/2+1]; out(cnt % 2 == 0 ? "P" : "K"); } } int main(){ sieve.request(mx); int t = 1; // in(t); while (t--) { solve(); } }