#include "gap.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
using namespace std;
void check_max(ll &a, ll b){ a = (b > a) ? b : a; }
const ll INF = 1e18;
const int INT_INF = 1e9;
int t, n;
ll solve_1(){
ll l, r, ans = 0;
MinMax(0, INF, &l, &r);
ll l2, r2;
n -= 2;
while(n > 0){
MinMax(l + 1, r - 1, &l2, &r2);
ans = max(ans, max(l2 - l, r - r2));
l = l2, r = r2;
n -= 2;
}
ans = max(ans, r - l);
return ans;
}
pair<ll, int> solve(ll l, ll r, int cnt, ll curr_mx){
if(r - l <= curr_mx) return {0, -1};
if(!cnt) return {0, 0};
ll mid = (l + r) >> 1, l2, r2, l3, r3;
MinMax(l + 1, mid, &l2, &r2);
MinMax(mid + 1, r - 1, &l3, &r3);
if(l2 == -1 && l3 == -1) return {r - l, 0};
if(l2 != -1) curr_mx = max(l2 - l, curr_mx);
else curr_mx = max(l3 - l, curr_mx);
if(r3 != -1) curr_mx = max(r - r3, curr_mx);
else curr_mx = max(r - r2, curr_mx);
if(l2 != -1 && l3 != -1) curr_mx = max(l3 - r2, curr_mx);
int new_cnt = 0;
if(l2 != -1){
auto p = solve(l2, r2, -1, curr_mx);
check_max(curr_mx, p.first);
if(p.second == -1){
new_cnt -= INT_INF;
cnt = -1;
}
if(cnt != -1) cnt -= p.second;
else new_cnt += p.second;
}
if(l3 != -1){
auto p = solve(l3, r3, cnt, curr_mx);
check_max(curr_mx, p.first);
if(p.second == -1){
new_cnt -= INT_INF;
cnt = -1;
}
if(cnt != -1) cnt -= p.second;
else new_cnt += p.second;
}
if(cnt == -1) new_cnt = -1;
if(new_cnt < 0) new_cnt = -1;
return {curr_mx, new_cnt};
}
ll findGap(int _t, int _n){
t = _t, n = _n;
if(t == 1) return solve_1();
if(n <= 1) return 0;
ll l, r;
MinMax(0, INF, &l, &r);
ll curr_mx = ((r - l) / (n - 1)) + !!((r - l) % (n - 1));
return max(solve(l, r, n - 2, curr_mx).first, curr_mx);
}
