#include <bits/stdc++.h>
#include "gap.h"
using namespace std;
typedef long long ll;
ll findGap1(int N) {
ll l = 1, r = N;
ll fl = LLONG_MIN, fr = LLONG_MAX;
ll arr[N+1];
while (l <= r) {
ll *q1 = new ll(0), *q2 = new ll(0);
MinMax(fl, fr, q1, q2);
arr[l++] = *q1;
arr[r--] = *q2;
fl = *q1+1;
fr = *q2-1;
}
ll ans = 0;
for (ll i = 1; i < N; i++) ans = max(ans, arr[i+1] - arr[i]);
return ans;
}
void query(ll s, ll t, ll &q1, ll &q2) {
ll *qr1 = new ll(0), *qr2 = new ll(0);
MinMax(s, t, qr1, qr2);
q1 = *qr1;
q2 = *qr2;
}
void rec(set<ll> &dt, ll l, ll r) {
if (l > r) return;
ll q1, q2;
query(l, r, q1, q2);
if (q1 == -1) return;
dt.insert(q1);
dt.insert(q2);
ll mid = (q1+q2)/2;
rec(dt, q1+1, q1 + (q2-q1+1)/3);
rec(dt, q1 + (q2-q1+1)/3 + 1, q1 + 2*(q2-q1+1)/3);
rec(dt, q1 + 2*(q2-q1+1)/3 + 1, q2-1);
}
ll findGap2(int N) {
set<ll> dt;
rec(dt, -2e18, 2e18);
vector<ll> arr;
for (ll i : dt) arr.push_back(i);
ll ans = 0;
for (ll i = 0; i < N-1; i++) ans = max(ans, arr[i+1] - arr[i]);
return ans;
}
ll findGap2_(int N) {
ll mi, mx;
query(LLONG_MIN, LLONG_MAX, mi, mx);
ll ans = (mx-mi+N-1)/N; // by pigeonhole
ll lst = mi, lft = N;
while (lst < mx && lft > 0) {
ll q1, q2;
query(lst+1, lst+ans, q1, q2);
if (q1 == -1) {
ll cq1, cq2;
query(lst+1, mx-1, cq1, cq2);
if (cq1 == -1) {
ans = max(ans, mx-lst);
lst = mx;
lft = 0;
} else {
ans = max({ans, cq1-lst, mx-cq2});
lst = cq1;
mx = cq2;
lft -= 2;
}
} else {
lst = q2;
lft--;
}
if (lft > 0) ans = max(ans, (mx-lst+lft-1)/lft);
}
return ans;
}
ll findGap(int T, int N) {
if (T == 1) return findGap1(N);
if (N <= 8) return findGap1(N);
//if (N <= 2016) return findGap2_(N);
return findGap2_(N);
}
