#include "hack.h"
#include <bits/stdc++.h>
using namespace std;
bool query (int l, int r){
int gap=sqrt(r-l+1);
vector<long long> v;
for (int i=1; i<=gap; ++i)
v.push_back(i);
for (int i=max(l+1,gap+1); i<=r; i+=gap)
v.push_back(i);
v.push_back(r+1);
return collisions(v);
}
int hack(){
int l=2,r=1000000000;
if (query(2,1000000))
r=1000000;
while (l<r){
int mid=l+r>>1;
if (query(1,mid-1))
l=mid+1;
else
r=mid;
}
return l;
}
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