#include "souvenirs.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ari2 = array<int, 2>;
using ari3 = array<int, 3>;
using arl2 = array<ll, 2>;
using arl3 = array<ll, 3>;
template <class T> using vt = vector<T>;
#define all(x) begin(x), end(x)
#define size(x) (int((x).size()))
#define REP(a,b,c,d) for(int a=(b);(d)>0?a<=(c):a>=(c);a+=(d))
#define FOR(a,b,c) REP(a,b,c,1)
#define ROF(a,b,c) REP(a,b,c,-1)
void buy_souvenirs(const int N, const ll P0) {
vt<ll> P(N);
P[0] = P0;
vt<int> cnt(N);
map<ll, pair<vt<int>, ll>> cache;
const auto ask = [&](const ll v) {
if (cache.find(v) != cache.end())
return cache[v];
const auto [vec, rem] = transaction(v);
for (const auto &j : vec)
cnt[j]++;
return make_pair(vec, v - rem);
};
ROF(i, N-1, 1) {
ll cur = P[0] - 1;
while (!P[i]) {
auto [vec, used] = ask(cur);
int n = size(vec);
for (const auto &j : vec)
used -= P[j], n -= j > i;
if (n == 1)
P[vec.back()] = used;
cur = (used + n - 1) / n - 1;
}
}
FOR(i, 1, N-1)
for (; cnt[i] < i; cnt[i]++)
transaction(P[i]);
}
