#include "gap.h"
#include<bits/stdc++.h>
#define pb push_back
using namespace std;
using ll = long long;
long long naive(int N)
{
long long l = 0, r = 1e18, lp = 0, rp = N-1, x=0, y=0, a[100100];
for(int i = 0; lp<=rp; i++) {
MinMax(l, r, &x, &y);
a[lp] = x, a[rp] = y;
l=x+1, r=y-1;
lp++,rp--;
}
ll ans = 0;
for(int i = 1; i < N; i++) {
ans = max(ans, a[i]-a[i-1]);
}
return ans;
}
long long findGap(int T, int N) {
if(T==1) {
return naive(N);
}
ll l = 0, r = 1e18, mn, mx, tl, tr, inc = 0;
MinMax(l, r, &mn, &mx);
ll step = (mx - mn + N - 1) / N;
l = mn, r = mn+step;
ll ans = step;
ll omx = mx;
vector<ll> x;
x.pb(mn);
mn++, mx--;
while (true) {
MinMax(l, r, &tl, &tr);
if (tl != -1) {
x.pb(tl);
x.pb(tr);
inc++;
}
if(tl!=-1)
for (int i = max(1, (int)x.size()-3); i < x.size(); i++) {
if(ans < x[i] - x[i - 1]) {
ans = x[i] - x[i - 1];
}
}
if(mx-tr<ans) break;
if (r == mx)
break;
l = r+1;
r = l+ans+1;
r = min(r, mx);
}
x.pb(omx);
for (int i = 1; i < x.size(); i++) {
if(ans < x[i] - x[i - 1]) {
ans = x[i] - x[i - 1];
}
}
return ans;
}
