#include "hack.h"
#include <vector>
#include <bits/stdc++.h>
#define pb push_back
#define lint long long int
using namespace std;
int hack(){
lint k = 500000;
while(k) {
auto ans = collisions({k,2*k});
if(ans == 1) break;
k--;
}
vector<lint> divisor;
for (int i = 2; i*i<=k;i++) {
if (k % i == 0) {divisor.pb(i);divisor.pb(k/i);}
}
sort(divisor.begin(),divisor.end());
//for (auto i: divisor) cout << i << " ";
//cout << "\n";
for (auto i: divisor) {
lint now = collisions({i,2*i});
if (now == 1) return i;
}
return k;
}
