#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 = 1, res, nn;
set < ll > q;
vector < ll > v;
vector < pair < ll, pll > > 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) {
q.insert(l);
q.insert(r);
if (r - l <= 1)
return;
if (l == r - 2) {
MinMax(l + 1, r - 1, &a, &b);
if (a == -1)
ans = max(ans, 2ll);
return;
}
ll y = 18;
y = min({r - l, y, nn - sz(q)});
y = max(y, 2ll);
vector < ll > v;
v.pb(l);
for (int x = 1; x < y; ++x)
v.pb(l + ((r - l) / y)*x);
v.pb(r - 1);
vector < pll > vv;
vv.pb({l, l});
for (int i = 1; i < sz(v); ++i) {
assert(v[i - 1] + 1 <= v[i]);
MinMax(v[i - 1] + 1, v[i], &a, &b);
if (a != -1)
vv.pb({a, b});
}
vv.pb({r, r});
for (int i = 1; i < sz(vv); ++i)
ans = max(ans, vv[i].f - vv[i - 1].s);
for (int i = 1; i < sz(vv) - 1; ++i) {
pll x = vv[i];
V.pb(mp(x.s - x.f, x));
}
}
long long findGap(int T, int n) {
nn = 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);
V.pb(mp(b - a, mp(a, b)));
ll iter = 1070;
while (sz(V)) {
ll j = getRand() % sz(V);
pair < ll, pll > cur = V[j];
if (cur.s.s - cur.s.f > ans) {
solve(cur.s.f, cur.s.s);
--iter;
}
if (!iter)
break;
swap(V[j], V.back());
V.ppb();
}
return ans;
}
