#include "hack.h"
#include "bits/stdc++.h"
#define pb push_back
#define dbg(X) cerr<<#X<<": "<<X<<endl
#define si(a_) (ll)(a_.size())
#define fi first
#define all(a_) a_.begin(),a_.end()
#define sc second
#define popb pop_back
#define ceri(a_,l_,r_) {for(ll i_ = l_;i_<=r_;i_++) cerr<<a_[i_]<< " ";cerr<<endl;}
using namespace std;
using ll = long long;
using pll = pair<ll,ll>;
ll n;
mt19937_64 rng(time(0));
ll rnd(ll l,ll r){return uniform_int_distribution<ll>(l,r)(rng);}
map<ll,bool> tu;
vector<ll> v,w;
ll mx = 1000000000;
/**
1
1000000000
**/
ll tres = 40000;
ll m = 31624;
vector<ll> con(vector<ll> a,vector<ll> b){
while(si(b)){
a.pb(b.back());
b.popb();
}
return a;
}
pll reshi(vector<ll> vl,vector<ll> vr){
// dbg(collisions(con(vl,vr)));
// cerr<<si(vl)<< " "<<si(vr)<<endl;
if(si(vl)==1&&si(vr)==1) return {vl[0],vr[0]};
vector<ll> vll,vlr;
vector<ll> vrl,vrr;
for(ll i = 0;i<si(vl);i++){
if(i<si(vl)/2) vll.pb(vl[i]);
else vlr.pb(vl[i]);
}
for(ll i = 0;i<si(vr);i++){
if(i<si(vr)/2) vrl.pb(vr[i]);
else vrr.pb(vr[i]);
}
if(collisions(con(vll,vrl))) return reshi(vll,vrl);
if(collisions(con(vll,vrr))) return reshi(vll,vrr);
if(collisions(con(vlr,vrl))) return reshi(vlr,vrl);
return reshi(vlr,vrr);
}
vector<ll> vl,vr;
int hack(){
ll c = -1;
if(collisions({1,2})) return 1;
ll mxv = 100*mx;
vector<ll> pw2;
pw2.pb(1);
while(pw2.back()<mx) pw2.pb(pw2.back()*2);
for(ll t = 0;;t++){
vl.clear(); vr.clear();
for(ll i = 1;i<=m;i++) vl.pb(i);
for(ll i = 2;i*m<=mx+m;i++) vr.pb(i*m);
if(collisions(con(vl,{m+1}))){
for(ll i = 3;i<=m+1;i++) if(collisions({1,i})) return i-1;
}
ll cnt = collisions(con(vl,vr));
//dbg(cnt);
if(cnt==0) continue;
//dbg(t);
// dbg(cnt);
//dbg(si(vl));
// dbg(si(vr));
pll p = reshi(vl,vr);
c = abs(p.fi-p.sc);
break;
}
//dbg(c);
ll ans = c;
vector<ll> d;
for(ll i = 2;i*i<=c;i++){
if(c%i==0){
//dbg(i);
d.pb(i);
if(i*i!=c){
//dbg(c/i);
d.pb(c/i);
}
}
}
d.pb(c);
sort(all(d));
for(ll x : d){
if(collisions({1,x+1})) return x;
}
return ans ;
}
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