#include "gap.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
const ll MOD = 998244353;
const ll INF = 1e18;
const ld EPS = 1e-12;
#define endl "\n"
#define sp <<" "<<
#define REP(i, a, b) for(ll i = a; i < b; i++)
#define dbg(x) cout << #x << " = " << x << endl
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fast_io() ios_base::sync_with_stdio(false); cin.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((ll)(x).size())
struct custom_hash {
	static uint64_t splitmix64(uint64_t x) {
		// http://xorshift.di.unimi.it/splitmix64.c
		x += 0x9e3779b97f4a7c15;
		x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
		x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
		return x ^ (x >> 31);
	}
	size_t operator()(uint64_t x) const {
		static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
		return splitmix64(x + FIXED_RANDOM);
	}
};
template <typename Key, typename Value>
using hash_map = unordered_map<Key, Value, custom_hash>;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// uniform_int_distribution<int>(a, b)(rng);
// shuffle(all(a), rng);
ll findGap(int T, int N) {
	auto decomp = [&](ll targ, pair<ll, ll> &a) -> vector<pair<ll, ll>> {
		vector<pair<ll, ll>> res;
		// adjust this (operations cap)
		ll now = a.second - a.first;
		// start of each is this
		ll len = (now + targ - 1) / targ;
		ll curr = a.first;
		while (curr + len < a.second) {
			res.push_back({curr, curr + len - 1});
			curr += len;
		}
		res.push_back({curr, a.second});
		return res;
	};
	
	auto query = [&](ll x, ll y, vector<ll> &nums, vector<pair<ll, ll>> &ranges) -> void {
		ll c, d;
		// cerr << "query: " << x sp y << endl;
		MinMax(x, y, &c, &d);
		if (c == -1 or d == -1) return;
		if (c == d) {
			nums.push_back(c);
		} else if (c + 1 == d) {
			nums.push_back(c);
			nums.push_back(d);
		} else {
			nums.push_back(c);
			nums.push_back(d);
			ranges.push_back({c+1, d-1});
		}
	};
	auto process = [&](vector<ll> &nums) -> ll {
		ll res = LLONG_MIN;
		sort(all(nums));
		REP(i, 1, N) res = max(res, nums[i] - nums[i-1]);
		return res;
	};
	if (T == 1) {
		ll a = 0, b = 1e18;
		vector<ll> nums;
		while ((int)nums.size() < N) {
			ll c, d;
			MinMax(a, b, &c, &d);
			nums.push_back(c);
			if (c != d) nums.push_back(d);
			a = c + 1;
			b = d - 1;
		}
		sort(all(nums));
		ll ans = LLONG_MIN;
		REP(i, 1, N) ans = max(ans, nums[i] - nums[i-1]);
		return ans;
	} else
	if (T == 2) {
		vector<ll> nums;
		vector<pair<ll, ll>> ranges, nranges, cranges;
		ranges.push_back({0, 1e18});
		ll ops = N / 2;
		vector<pair<ll, ll>> nwe = decomp(ops, ranges[0]);
		for (auto &[x, y] : nwe) {
			query(x, y, nums, nranges);
		}
		while (nums.size() < N) {
			ops = (N - nums.size()) / 2;
			ll targ = (ops + nranges.size() - 1) / ll(nranges.size());
			ll amt = targ * ll(nranges.size());
			ranges.clear();
			nranges.swap(ranges);
			for (auto &cc : ranges) {
				nwe = decomp(targ, cc);
				for (auto &[x, y] : nwe) {
					query(x, y, nums, nranges);
				}
			}
		}
		return process(nums);
	}
	return 0;
}
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