#include "hack.h"
#include<bits/stdc++.h>
#define pb push_back
#define F first
#define S second
#define str string
#define ll long long
#define ull unsigned ll
#define ld long double
#define pll pair<ll,ll>
#define plll pair<ll,pll>
#define pllll pair<pll,pll>
#define pii pair<int,int>
#define vl vector<ll>
#define vll vector<pll>
#define vlll vector<plll>
#define vllll vector<p4>
#define vi vector<int>
#define vii vector<pii>
#define sz(x) (ll)(x).size()
#define fr front()
#define tp top()
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define ins insert
#define m_p make_pair
#pragma GCC target( "sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("Ofast,unroll-loops,fast-math,O3")
using namespace std;
const ld pi=acos(-1.0);
const ll e5=1e5, e6=1e6, e9=1e9;
const ll inf=1e18;
const ll mod=998244353;
const ll MOD=106710087877475399;
const ll N=1e6+10;
const ll M=2e5+10;
const ld eps=1e-9;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll bpm(ll x,ll y,ll m){if(y==0)return 1%m;ll p=bpm(x,y/2,m);
if(y%2==0)return p*p%m;else return p*p%m*x%m;}
ll bp(ll x,ll y){if(y==0)return 1;ll p=bp(x,y/2);
if(y%2==0)return p*p;else return p*p*x;}
int hack(){
ll l=5e8,r=1e9,m;
while(l<r){
m=(l+r)/2;
vl v;
ll x=1;
while((m-l+x+1)/(x+1)+x+1 <= (m-l+x+1)/x+x) x++;
for(ll i=1;i<=x;i++) v.pb(i);
for(ll i=l+x;i<=m;i+=x) v.pb(i);
v.pb(m+1);
ll s=collisions(v);
if(s>0) r=m;
else l=m+1;
}
set<ll> st;
for(ll i=1;i*i<=l;i++){
if(l%i==0){
st.ins(i);
st.ins(l/i);
}
}
for(ll x:st){
if(x>=l) break;
ll s=collisions({1,x+1});
if(s>0){ l=x; break;}
}
return l;
}
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