#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;
// optimize this first N query by decomposing the range into first found from left and first found from right
// {
// query(ll(0), ll(1e18), nums, ranges);
// }
ranges.push_back({0, 1e18});
ll ops = max(1, N/8);
vector<pair<ll, ll>> nwe = decomp(ops, ranges[0]);
for (auto &[x, y] : nwe) {
query(x, y, nums, nranges);
}
while (nums.size() < N) {
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;
}
