#include "light.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
ll len = 1;
vl s = {1};
vector<pll> segs2;
vector<pll> segs;
void prepare()
{
}
pair<ll,vl> join(ll p)
{
len += p;
segs2 = {};
segs = {};
forall(it,s)
{
if(it > len) break;
segs.pb({it,min(len,it+p)});
}
ll pop_first = -1;
ll pop_second = -1;
forall(it,segs)
{
if(it.ff <= pop_second)
{
pop_second = max(pop_second,it.ss);
}
else
{
if(pop_second != -1) segs2.pb({pop_first,pop_second});
pop_first = it.ff;
pop_second = it.ss;
}
}
segs2.pb({pop_first,pop_second});
segs = segs2;
ll cur = len-1;
s = {len};
if(len != 1)
{
s.pb(len-1);
}
while(cur > 1)
{
ll pop = cur - (len-cur);
ll best = 1e18;
forall(it,segs)
{
if(it.ss >= pop)
{
best = min(best,max(it.ff,pop));
}
}
s.pb(best);
cur = best;
}
sort(all(s));
return {p,s};
}
pair<ll,vl> leave(ll p)
{
len -= p;
segs2 = {};
segs = {};
forall(it,s)
{
if(it > len) break;
segs.pb({it,min(len,it+p)});
}
ll pop_first = -1;
ll pop_second = -1;
forall(it,segs)
{
if(it.ff <= pop_second)
{
pop_second = max(pop_second,it.ss);
}
else
{
if(pop_second != -1) segs2.pb({pop_first,pop_second});
pop_first = it.ff;
pop_second = it.ss;
}
}
segs2.pb({pop_first,pop_second});
segs = segs2;
ll cur = len-1;
s = {len};
if(len != 1)
{
s.pb(len-1);
}
while(cur > 1)
{
ll pop = cur - (len-cur);
ll best = 1e18;
forall(it,segs)
{
if(it.ss >= pop)
{
best = min(best,max(it.ff,pop));
}
}
s.pb(best);
cur = best;
}
sort(all(s));
return {p,s};
}
