#include "gap.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define mp make_pair
#define lsb(x) (x&(-x))
#define pii pair<int,int>
#define ss second
#define ff first
#define piii pair<int,pii>
#define debu(x) (cerr << #x << " = "<< x << "\n")
#define debu2(x,y) (cerr << #x << " = "<< x << " " << #y << " = " << y << "\n")
#define debu3(x,y,z) (cerr << #x << " = "<< x << " " << #y << " = " << y << " " << #z << " = " << z<< "\n")
#define bitout(x,y) {\
cerr << #x << " : ";\
for (int justforbits = y; justforbits >=0; justforbits--)cout << (((1 << justforbits) & x)>=1);\
cout << "\n";\
}
#define rangeout(j,rangestart,rangeend) {\
cerr << "outputting " << #j<< ":\n";\
for (int forrang = rangestart; forrang <= rangeend; forrang++)cerr << j[forrang] << " ";\
cerr<<"\n";\
}
#define c1 {cerr << "Checkpoint 1! \n\n";cerr.flush();}
#define c2 {cerr << "Checkpoint 2! \n\n";cerr.flush();}
#define c3 {cerr << "Checkpoint 3! \n\n";cerr.flush();}
#define c4 {cerr << "Checkpoint 4! \n\n";cerr.flush();}
#define vi vector<int>
#define vpii vector<pii>
#define fr(i,x,y) for(int i=x;i<=y;i++)
#define pf push_front;
//for some reason cannot use sets???
long long findGap(int T, int N)
{
#define int long long
vi nums;int t1,t2;
vector<vector<pii>>ranges;
vector<pii>t5;t5.pb(mp(0,1e18));
ranges.pb(t5);
while(nums.size()<N)
{
vector<pii>t6;
for(pii rr:ranges.back())
{
MinMax(rr.ff,rr.ss,&t1,&t2);
if(t1!=t2){nums.pb(t1);}nums.pb(t2);
if(t2-t1-1<2)continue;
if(t2-t1-1==2){t6.pb(mp(t1+1,t2-1));}
else
{
int mid=(t1+t2)/2;
t6.pb(mp(t1+1,mid));t6.pb(mp(mid+1,t2-1));
}
}
ranges.pb(t6);
}
sort(nums.begin(),nums.end());
int ans=0;
for(int i=1;i<nums.size();i++)
{
ans=max(nums[i]-nums[i-1],ans);
}
return ans;
#undef int
}
