#include "hack.h"
#include <bits/stdc++.h>
using namespace std;
const int BLK = 31622;
#define int long long
#define pii pair<int, int>
#define mp make_pair
#define pb push_back
#define fi first
#define se second
signed hack(){
vector<int> a, b;
for (int i=1; i<=BLK; ++i)a.pb(i);
for (int i=500000000; i<=1000000000+BLK; i+=BLK)b.pb(i);
while (a.size()>1||b.size()>1){
if (a.size()<b.size())swap(a, b);
vector<int> l, r, temp;
for (int i=0; i<a.size()/2; ++i)l.pb(a[i]), temp.pb(a[i]);
for (int i=a.size()/2; i<a.size(); ++i)r.pb(a[i]);
for (auto c:b)temp.pb(c);
if (collisions(temp))a=l;
else a=r;
}
int n=abs(a[0]-b[0]), v=n, c=2;
vector<int> vect;
while (c*c<=v){
if (!(v%c))v/=c, vect.pb(c);
else ++c;
}
if (v!=1)vect.pb(v);
for (auto c:vect)if (collisions({1, n/c+1}))n/=c;
return n;
}
