#include <bits/stdc++.h>
#include "souvenirs.h"
#include <utility>
#include <vector>
using namespace std;
using ll = long long;
using ld = long double;
#define fi first
#define se second
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int, int>
#define pll pair<long long, long long>
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::high_resolution_clock::now().time_since_epoch().count());
inline int rand(int l,int r){return uniform_int_distribution<int>(l, r)(rng);}
inline ll rand(ll l,ll r){return uniform_int_distribution<ll>(l, r)(rng64);}
#ifdef DEBUG
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
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);
}
};
struct pair_hash{
size_t operator()(const pair<int,int>&x)const{
return hash<long long>()(((long long)x.first)^(((long long)x.second)<<32));
}
};
//pair<vector<int>, long long> transaction(long long M){}
vi cnt;
vi known;
vll a;
int N;
//(ll)S / (i + 1) - ((S % (i + 1)) == 0)
ll getBound(int x, ll S){
if(x == 1){
return S;
}
return (ll)(S - x * (x - 1) / 2) / x;
}
void f(vi curr, ll S){
//cerr << sz(curr) << ' ' << curr[0] << ' ' << S << '\n';
if(sz(curr) == 1){
known[curr[0]] = 1;
a[curr[0]] = S;
if(curr[0] == N - 1 || known[curr[0] + 1]){
return;
}
//cerr << curr[0] << ' ' << S << '\n';
pair<vi, ll> x = transaction(a[curr[0]] - 1);
for(auto ele : x.fi){
cnt[ele]++;
}
f(x.fi, a[curr[0]] - 1 - x.se);
return;
}
for(int i = sz(curr) - 1; i >= 0; i--){
if(i == 0){
vi X = {curr[i]};
f(X, S);
continue;
}
if(known[curr[i]]){
S -= a[curr[i]];
continue;
}
ll B = getBound(i + 1, S);
pair<vi, ll> x = transaction(B);
for(auto ele : x.fi){
cnt[ele]++;
}
f(x.fi, B - x.se);
S -= a[curr[i]];
}
}
void buy_souvenirs(int n, ll P0) {
N = n;
cnt.assign(N, 0);
known.assign(N, 0);
a.assign(N, -1);
a[0] = P0;
known[0] = 1;
vi curr = {0};
f(curr, P0);
for(int i = 1; i < N; i++){
while(cnt[i] < i){
transaction(a[i]);
cnt[i]++;
}
}
}
// int main(){
// // ios_base::sync_with_stdio(0);
// // cin.tie(NULL);
// // cout.tie(NULL);
// int t = 1;
// cin >> t;
// while(t--){
// solve();
// }
// return 0;
// }
