#ifdef NACHIA #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #include #include #include #include #include #include #include #include #include namespace nachia{ long long CountingPrimes(long long maxval){ using i64 = long long; i64 n = maxval; if(n <= 1) return 0; i64 sqrtn = 0; while(sqrtn * sqrtn <= n) sqrtn++; sqrtn--; std::vector prefix_sum_fairy(sqrtn+1, 0); for(i64 i=1; i<=sqrtn; i++) prefix_sum_fairy[i] = i-1; std::vector prefix_sum_devil(sqrtn+1, 0); for(i64 i=1; i<=sqrtn; i++) prefix_sum_devil[i] = n/i-1; for(i64 p=2; p<=sqrtn; p++){ i64 prime_count_p = prefix_sum_fairy[p]; i64 prime_count_p_minus1 = prefix_sum_fairy[p-1]; if(prime_count_p == prime_count_p_minus1) continue; for(i64 devil_id = 1; devil_id <= sqrtn; devil_id++){ if(devil_id * p <= sqrtn){ prefix_sum_devil[devil_id] -= prefix_sum_devil[devil_id * p] - prime_count_p_minus1; } else{ i64 tg_fairy = n / (devil_id * p); if(tg_fairy < p) break; prefix_sum_devil[devil_id] -= prefix_sum_fairy[tg_fairy] - prime_count_p_minus1; } } for(i64 fairy_id = sqrtn/p; fairy_id >= p; fairy_id--){ i64 dc = prefix_sum_fairy[fairy_id] - prime_count_p_minus1; i64 max_tg = std::min(fairy_id * p + p - 1, sqrtn); for(i64 tg_fairy = fairy_id * p; tg_fairy <= max_tg; tg_fairy++) prefix_sum_fairy[tg_fairy] -= dc; } } return prefix_sum_devil[1]; } } // namespace nachia using i64 = long long; using u64 = unsigned long long; #define rep(i,n) for(int i=0; i=0; i--) const i64 INF = 1001001001001001001; const char* yn(bool x){ return x ? "Yes" : "No"; } template void chmin(A& l, const A& r){ if(r < l) l = r; } template void chmax(A& l, const A& r){ if(l < r) l = r; } template using nega_queue = std::priority_queue,std::greater>; using Modint = atcoder::static_modint<998244353>; //#include "nachia/vec.hpp" using namespace std; void unit(){ int N; cin >> N; int n = N/2+1; int c = N - 1 - nachia::CountingPrimes(N-1) + nachia::CountingPrimes(n-1); cout << (c%2 == 0 ? "K\n" : "P\n"); } void testcase(){ int T; cin >> T; rep(t,T) unit(); } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); #ifdef NACHIA int T; cin >> T; for(int t=0; t