#include "gap.h"
#include <bits/stdc++.h>
typedef long long ll;
typedef long double ld;
using namespace std;
ll findSmall(int N) {
vector <ll> v (N);
ll mn, mx;
MinMax (1, 1e18, &mn, &mx);
ll s = mn, e = mx;
v[0] = s, v[N-1] = e;
int l = 0, r = N - 1;
while (l + 1 < r) {
MinMax(v[l] + 1, v[r] - 1, &s, &e);
v[++l] = s, v[--r] = e;
}
for (int i = 1; i < N; i++) {
v[i-1] = v[i] - v[i-1];
}
return *max_element(v.begin(), v.end() - 1);
}
ll findGap(int T, int N) {
if (T == 1) {
return findSmall(N);
}
ll mn, mx;
MinMax (1, 1e18, &mn, &mx);
ll s = mn, e = mx;
ld d = (ld) (mx - mn - 2) / N;
ld l = mn + 1, r = mn + 1 + d;
ll gap = 0, mx_old = mn, last_ir = s;
for (int i = 0; i < N - 1; i++) {
ll il = ceil (l - 1e-7) + (ceil (l - 1e-7) == last_ir), ir = floor (r + 1e-7);
//cout << il << ' ' << ir << endl;
if (il > ir) continue;
last_ir = ir;
MinMax(il, ir, &mn, &mx);
//cout << ' ' << mn << ' ' << mx << endl;
if (mn != -1) {
gap = max (gap, mn - mx_old);
mx_old = mx;
}
l += d, r += d;
}
ll il = ceil (l - 1e-7) + (ceil (l + 1e-7) == mx_old), ir = floor (r + 1e-7);
//cout << il << ' ' << ir << endl;
if (il <= ir) MinMax(il, ir, &mn, &mx);
//cout << ' ' << mn << ' ' << mx << endl;
if (mn != -1 && il <= ir) {
gap = max (gap, mn - mx_old);
mx_old = mx;
}
gap = max (gap, e - mx_old);
return gap;
}
