#include using namespace std; typedef long long ll; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b #define vl vector #define vii vector> #define vll vector> #define vvi vector> #define vvl vector> #define vvii vector>> #define vvll vector>> #define vst vector #define pii pair #define pll pair #define pb push_back #define all(x) (x).begin(),(x).end() #define mkunique(x) sort(all(x));(x).erase(unique(all(x)),(x).end()) #define fi first #define se second #define mp make_pair #define si(x) int(x.size()) const int mod=998244353,MAX=10000005,INF=15<<26; //高速素因数分解 /** * Author: chilli, Ramchandra Apte, Noam527, Simon Lindholm * Date: 2019-04-24 * License: CC0 * Source: https://github.com/RamchandraApte/OmniTemplate/blob/master/modulo.hpp… * Description: Calculate $a\cdot b\bmod c$ (or $a^b \bmod c$) for $0 \le a, b \le c \le 7.2\cdot 10^{18}$. * Time: O(1) for \texttt{modmul}, O(\log b) for \texttt{modpow} * Status: stress-tested, proven correct * Details: * This runs ~2x faster than the naive (__int128_t)a * b % M. * A proof of correctness is in doc/modmul-proof.tex. An earlier version of the proof, * from when the code used a * b / (long double)M, is in doc/modmul-proof.md. * The proof assumes that long doubles are implemented as x87 80-bit floats; if they * are 64-bit, as on e.g. MSVC, the implementation is only valid for * $0 \le a, b \le c < 2^{52} \approx 4.5 \cdot 10^{15}$. */ #pragma once typedef unsigned long long ull; ull modmul(ull a, ull b, ull M) { ll ret = a * b - M * ull(1.L / M * a * b); return ret + M * (ret < 0) - M * (ret >= (ll)M); } ull modpow(ull b, ull e, ull mod) { ull ans = 1; for (; e; b = modmul(b, b, mod), e /= 2) if (e & 1) ans = modmul(ans, b, mod); return ans; } /** * Author: chilli, SJTU, pajenegod * Date: 2020-03-04 * License: CC0 * Source: own * Description: Pollard-rho randomized factorization algorithm. Returns prime * factors of a number, in arbitrary order (e.g. 2299 -> \{11, 19, 11\}). * Time: $O(n^{1/4})$, less for numbers with small factors. * Status: stress-tested * * Details: This implementation uses the improvement described here * (https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm#Variants…), where * one can accumulate gcd calls by some factor (40 chosen here through * exhaustive testing). This improves performance by approximately 6-10x * depending on the inputs and speed of gcd. Benchmark found here: * (https://ideone.com/nGGD9T) * * GCD can be improved by a factor of 1.75x using Binary GCD * (https://lemire.me/blog/2013/12/26/fastest-way-to-compute-the-greatest-common-divisor/…). * However, with the gcd accumulation the bottleneck moves from the gcd calls * to the modmul. As GCD only constitutes ~12% of runtime, speeding it up * doesn't matter so much. * * This code can probably be sped up by using a faster mod mul - potentially * montgomery reduction on 128 bit integers. * Alternatively, one can use a quadratic sieve for an asymptotic improvement, * which starts being faster in practice around 1e13. * * Brent's cycle finding algorithm was tested, but doesn't reduce modmul calls * significantly. * * Subtle implementation notes: * - we operate on residues in [1, n]; modmul can be proven to work for those * - prd starts off as 2 to handle the case n = 4; it's harmless for other n * since we're guaranteed that n > 2. (Pollard rho has problems with prime * powers in general, but all larger ones happen to work.) * - t starts off as 30 to make the first gcd check come earlier, as an * optimization for small numbers. */ #pragma once /** * Author: chilli, c1729, Simon Lindholm * Date: 2019-03-28 * License: CC0 * Source: Wikipedia, https://miller-rabin.appspot.com * Description: Deterministic Miller-Rabin primality test. * Guaranteed to work for numbers up to $7 \cdot 10^{18}$; for larger numbers, use Python and extend A randomly. * Time: 7 times the complexity of $a^b \mod c$. * Status: Stress-tested */ #pragma once bool isPrime(ull n) { if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3; ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}, s = __builtin_ctzll(n-1), d = n >> s; for (ull a : A) { // ^ count trailing zeroes ull p = modpow(a%n, d, n), i = s; while (p != 1 && p != n - 1 && a % n && i--) p = modmul(p, p, n); if (p != n-1 && i != s) return 0; } return 1; } ull pollard(ull n) { auto f = [n](ull x) { return modmul(x, x, n) + 1; }; ull x = 0, y = 0, t = 30, prd = 2, i = 1, q; while (t++ % 40 || __gcd(prd, n) == 1) { if (x == y) x = ++i, y = f(x); if ((q = modmul(prd, max(x,y) - min(x,y), n))) prd = q; x = f(x), y = f(f(y)); } return __gcd(prd, n); } vector factor(ull n) { if (n == 1) return {}; if (isPrime(n)) return {n}; ull x = pollard(n); auto l = factor(x), r = factor(n / x); l.insert(l.end(), all(r)); return l; } vector prime;//i番目の素数 bool is_prime[MAX+1]; void sieve(int n){ for(int i=0;i<=n;i++){ is_prime[i]=true; } is_prime[0]=is_prime[1]=false; for(int i=2;i<=n;i++){ if(is_prime[i]){ prime.push_back(i); for(int j=2*i;j<=n;j+=i){ is_prime[j] = false; } } } } int main(){ std::ifstream in("text.txt"); std::cin.rdbuf(in.rdbuf()); cin.tie(0); ios::sync_with_stdio(false); sieve(MAX-2); vl X; for(ll p:prime){ if(is_prime[p+2]){ X.pb(p*(p+2)); } } int Q;cin>>Q; while(Q--){ ll N;cin>>N; auto it=upper_bound(all(X),N); if(it!=X.begin()){ it--; cout<<(*it)<<"\n"; }else{ cout<<-1<<"\n"; } } }