#include "gap.h"
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ldb;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<ldb,ldb> pdd;
#define ff(i,a,b) for(int i = a; i <= b; i++)
#define fb(i,b,a) for(int i = b; i >= a; i--)
#define trav(a,x) for (auto& a : x)
#define sz(a) (int)(a).size()
#define fi first
#define se second
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
// os.order_of_key(k) the number of elements in the os less than k
// *os.find_by_order(k) print the k-th smallest number in os(0-based)
const int mod = 1000000007;
const ll inf = 1e18;
const int mxN = 200005;
int N;
ll findGap(int T, int _N){
N = _N;
if(T == 1){
ll P = 0, Z = 0;
MinMax(0, inf, &P, &Z);
vector<ll> vec; vec.pb(P);
ff(i,2,N - 1){
ll S = 0, Q = 0;
MinMax(P + 1, Z, &S, &Q);
if(S != -1)vec.pb(S), P = S;
}
vec.pb(Z);
ll mx = 0;
ff(i,1,sz(vec) - 1)mx = max(mx, vec[i] - vec[i - 1]);
return mx;
}
else{
ll P = 0, Z = 0;
MinMax(0, inf, &P, &Z);
if(N == 2){
return Z - P;
}
ll D = (Z - P - 1 + N - 2) / (N - 1);
vector<ll> vec; vec.pb(P);
for(ll X = P + 1; X < Z; X += D){
ll L = X;
ll R = min(Z - 1, X + D - 1);
ll S = 0, Q = 0;
MinMax(L, R, &S, &Q);
if(S != -1)vec.pb(S);
if(Q != -1)vec.pb(Q);
}
vec.pb(Z);
ll mx = 0;
ff(i,1,sz(vec) - 1){
mx = max(mx, vec[i] - vec[i - 1]);
}
return mx;
}
}
// int main() {
// cin.tie(0)->sync_with_stdio(0);
// cin >> N;
// ff(i,1,N)cin >> A[i];
// cout << findGap(1, N) << '\n';
// return 0;
// }
/*
4
2 3 6 8
// probati bojenje sahovski
*/
