#include "gap.h"
#include<bits/stdc++.h>
#define ios ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define dec(x, y) fixed << setprecision((y)) << (x)
#define xx first
#define yy second
#define srt(v) sort((v).begin(), (v).end())
#define srtr(v) sort((v).rbegin(), (v).rend())
#define pb push_back
#define popb pop_back
#define sz(a) (int)(a).size()
#define len(a) (int)(a).length()
#define mp make_pair
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const ll maks=(ll)1e18;
/*ll b[100002];
int m;
void MinMax(ll s, ll t, ll &mn, ll &mx) {
int it=lower_bound(b, b+m, s)-b;
int it1=lower_bound(b, b+m, t+1)-1-b;
if(it1<it) {mn=mx=-1;}
else {mn=b[it]; mx=b[it1];}
}*/
ll findGap(int T, int N) {
int n=N;
if(T==1) {
ll a[100002];
ll mini=0LL, maxi=maks+1LL;
for(int i=0; i<(n+1)/2; ++i) {
MinMax(mini+1, maxi-1, &mini, &maxi);
a[i]=mini;
a[n-i-1]=maxi;
}
maxi=0LL;
for(int i=1; i<n; ++i) {
maxi=max(maxi, a[i]-a[i-1]);
}
return maxi;
}
ll mini, maxi;
MinMax(1LL, maks, &mini, &maxi);
vector<ll> v;
v.pb(mini); v.pb(maxi);
ll x=ceil((double)(maxi-mini+1LL)/(double)((ll)n-1LL));
ll mn1, mx1;
for(int i=0;; ++i) {
if(mini+(ll)i*x>=maxi) break;
MinMax((i==0?1LL:0LL)+mini+(ll)i*x, min(mini+(ll)(i+1)*x-1LL, maxi-1LL), &mn1, &mx1);
v.pb(mn1); v.pb(mx1);
}
srt(v);
maxi=0LL;
for(int i=1; i<sz(v); ++i) {
maxi=max(maxi, v[i]-v[i-1]);
}
return maxi;
}
/*int main() {
cin >> m;
for(int i=0; i<m; ++i) {
cin >> b[i];
}
cout << findGap(2, m);
return 0;
}*/
