#include "gap.h"
#include <bits/stdc++.h>
#define ll long long
using namespace std;
/*
static void my_assert(int k){ if (!k) exit(1); }
static int subtask_num, N;
static long long A[100001];
static long long call_count;
long long findGap(int, int);
void MinMax(long long s, long long t, long long *mn, long long *mx)
{
int lo = 1, hi = N, left = N+1, right = 0;
my_assert(s <= t && mn != NULL && mx != NULL);
while (lo <= hi){
int mid = (lo+hi)>>1;
if (A[mid] >= s) hi = mid - 1, left = mid;
else lo = mid + 1;
}
lo = 1, hi = N;
while (lo <= hi){
int mid = (lo+hi)>>1;
if (A[mid] <= t) lo = mid + 1, right = mid;
else hi = mid - 1;
}
if (left > right) *mn = *mx = -1;
else{
*mn = A[left];
*mx = A[right];
}
if (subtask_num == 1) call_count++;
else if (subtask_num == 2) call_count += right-left+2;
}
*/
ll l2=0,r2=1e18;
ll *l1=&l2;
ll *r1=&r2;
vector <ll> vec;
set <ll> st;
ll n,q;
ll s(ll m)
{
vector<ll> vec;
ll l=0,r=1e18;
l2=0,r2=1e18;
while(l<=r&&m--){
MinMax(l,r,l1,r1);
if(l2!=-1)vec.push_back(l2);
if(r2!=-1)vec.push_back(r2);
l=l2;
r=r2;
l++;
r--;
}
sort(vec.begin(),vec.end());
ll ans=1;
for(ll i=1;i<vec.size();i++)ans=max(ans,vec[i]-vec[i-1]);
return ans;
}
void bs(ll l,ll r)
{
if(l>r||n==0)return;
ll mid=(l+r)/2;
// cout<<l<<" "<<mid<<endl;
MinMax(l,mid,l1,r1);
// cout<<l2<<" "<<r2<<endl;
if(l2==-1){
bs(mid+1,r);
}
else if(l2==r2){
vec.push_back(l2);
n--;
st.insert(l2);
bs(mid+1,r);
}
else if(l2+1==r2){
vec.push_back(l2);
vec.push_back(r2);
n-=2;
st.insert(l2);
st.insert(r2);
bs(mid+1,r);
}
else{
n-=2;
vec.push_back(l2);
vec.push_back(r2);
bs(l2+1,r2-1);
bs(mid+1,r);
}
}
ll s2()
{
st.clear();vec.clear();
ll l=0;
ll r=1e18;
bs(l,r);
ll ans=1;
sort(vec.begin(),vec.end());
for(ll i=1;i<vec.size();i++)ans=max(ans,vec[i]-vec[i-1]);
//for(auto x:vec)cout<<x<<" ";cout<<endl;
return ans;
}
long long findGap(int T, int N)
{
n=N;
q=1;
if(T==1)return s((N+1)/2);
else{
return s2();
}
}
/*
int main()
{
FILE *in = stdin, *out = stdout;
my_assert(2 == fscanf(in, "%d%d", &subtask_num, &N));
my_assert(1 <= subtask_num && subtask_num <= 2);
my_assert(2 <= N && N <= 100000);
for (int i=1;i<=N;i++) my_assert(1 == fscanf(in, "%lld", A+i));
for (int i=1;i<N;i++) my_assert(A[i] < A[i+1]);
fprintf(out, "%lld\n", findGap(subtask_num, N));
fprintf(out, "%lld\n", call_count);
}
*/
