#include "gap.h"
/*
* Author: Nonoze
* Created: Friday 12/12/2025
*/
#include <bits/stdc++.h>
using namespace std;
#ifndef DEBUG
#define dbg(...)
#endif
// #define cout cerr << "OUT: "
#define endl '\n'
#define endlfl '\n' << flush
#define quit(x) return (void)(cout << x << endl)
template<typename T> void read(T& x) { cin >> x; }
template<typename T1, typename T2> void read(pair<T1, T2>& p) { read(p.first), read(p.second); }
template<typename T> void read(vector<T>& v) { for (auto& x : v) read(x); }
template<typename T1, typename T2> void read(T1& x, T2& y) { read(x), read(y); }
template<typename T1, typename T2, typename T3> void read(T1& x, T2& y, T3& z) { read(x), read(y), read(z); }
template<typename T1, typename T2, typename T3, typename T4> void read(T1& x, T2& y, T3& z, T4& zz) { read(x), read(y), read(z), read(zz); }
template<typename T> void print(vector<T>& v) { for (auto& x : v) cout << x << ' '; cout << endl; }
#define sz(x) (int)(x.size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define make_unique(v) sort(all(v)), v.erase(unique(all(v)), (v).end())
#define pb push_back
#define mp(a, b) make_pair(a, b)
#define fi first
#define se second
#define cmin(a, b) a = min(a, b)
#define cmax(a, b) a = max(a, b)
#define YES cout << "YES" << endl
#define NO cout << "NO" << endl
#define QYES quit("YES")
#define QNO quit("NO")
#define int long long
#define double long double
const int inf = numeric_limits<int>::max() / 4;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int MOD = 1e9+7, LOG=20;
int findGap(signed type, signed n) {
if (type==1) {
int mn=0, mx=1e18;
vector<int> beg, end;
while (n>0) {
int nmin, nmax; MinMax(mn, mx, &nmin, &nmax);
beg.pb(nmin);
end.pb(nmax);
mn=nmin+1;
mx=nmax-1;
n-=2;
}
reverse(all(end));
vector<int> a=beg; a.insert(a.end(), all(end));
int ans=0;
for (int i=1; i<sz(a); i++) cmax(ans, a[i]-a[i-1]);
return ans;
}
int mn=0, mx=1e18; MinMax(mn, mx, &mn, &mx);
int prec=mn;
int sz=(mx-mn+1)/n, ans=sz;
mn++, mx--;
while (mn<=mx) {
int nmin, nmax; MinMax(mn, mn+sz-1, &nmin, &nmax);
if (nmin!=-1) {
cmax(ans, nmin-prec);
prec=nmax;
}
mn+=sz;
}
cmax(ans, mx+1-prec);
return ans;
}
