#include "hack.h"
#include <bits/stdc++.h>
#define ll long long
#define dbg(x) cerr << #x << ' ' << x << endl;
using namespace std;
ll val(ll l, ll r)
{
ll m=sqrt(r-l+1);
vector<ll> v;
for (int i=1;i<=m;i++)
{
v.push_back(i);
}
for (int i=m+l;i<=r;i+=m)
{
v.push_back(i);
}
if(v.back() < r) v.push_back(r);
return collisions(v);
}
int hack(){
ll l=2;
ll r=1e9;
while (l<r)
{
ll mid=ceil((l+r)/2.0);
if(val(l,mid)>=1)
{
r=mid-1;
}
else
{
l=mid;
}
}
return l;
}
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