#include "gap.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
//#define int long long
//#pragma GCC optimize("Ofast")
//#pragma comment(linker, "/stack:200000000")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4")
#define file(s) freopen(s".in","r",stdin); freopen(s".out","w",stdout);
#define fastio ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
#define all(x) x.begin(), x.end()
#define sz(s) (int)s.size()
#define pb push_back
#define ppb pop_back
#define mp make_pair
#define s second
#define f first
typedef pair < long long, long long > pll;
typedef pair < int, int > pii;
typedef unsigned long long ull;
typedef vector < pii > vpii;
typedef vector < int > vi;
typedef long double ldb;
typedef long long ll;
typedef double db;
typedef tree < int, null_type, less < int >, rb_tree_tag, tree_order_statistics_node_update > ordered_set;
const int inf = 1e9, maxn = 2e5 + 48, mod = 998244353, N = 2e5 + 12;
const int dx[] = {1, -1, 0, 0}, dy[] = {0, 0, 1, -1}, block = 300;
const pii base = mp(1171, 3307), Mod = mp(1e9 + 7, 1e9 + 9);
const db eps = 1e-12, pi = acos(-1);
const ll INF = 1e18;
ll a, b, ans, res;
set < ll > q;
vector < ll > v;
ll getRand () {
ll res = 0;
for (int x = 0; x < 61; ++x)
if (rand() & 1)
res |= (1ll << x);
return res;
}
void solve (ll l, ll r) {
if (l >= r)
return;
ll m = (l + r) / 2;
ll a1, b1, a2, b2;
if (l + 1 <= m)
MinMax(l + 1, m, &a1, &b1);
else
a1 = b1 = -1;
if (m + 1 <= r - 1)
MinMax(m + 1, r - 1, &a2, &b2);
else
a2 = b2 = -1;
if (a1 == -1)
b1 = l;
if (b2 == -1)
a2 = r;
ans = max(ans, a2 - b1);
if (a1 != -1 && b1 - a1 > ans)
solve(a1, b1);
if (b2 != -1 && b2 - a2 > ans)
solve(a2, b2);
}
void solve1 (ll l, ll r) {
// cerr << l << ' ' << r << endl;
if (l > r || l == -1)
return;
MinMax(l, r, &a, &b);
if (a == -1)
return;
v.pb(a);
v.pb(b);
++a, --b;
if (a > b)
return;
l = a, r = b;
ll m = (l + r) / 2;
solve1(l, m);
solve1(m + 1, r);
}
long long findGap(int T, int n) {
srand(time(0));
if (T == 1) {
ll l = 0, r = INF;
vector < ll > v;
while (l <= r) {
if (sz(v) >= n)
break;
MinMax(l, r, &a, &b);
v.pb(a);
v.pb(b);
l = a + 1;
r = b - 1;
}
sort(all(v));
ll ans = 0;
for (ll i = 1; i < sz(v); ++i)
ans = max(ans, v[i] - v[i - 1]);
return ans;
}
MinMax(0, INF, &a, &b);
solve(a, b);
solve1(a, b);
sort(all(v));
for (ll i = 1; i < sz(v); ++i)
res = max(res, v[i] - v[i - 1]);
assert(res == ans);
return ans;
}
