#include <bits/stdc++.h>
#include "souvenirs.h"
using namespace std;
struct Equation {
vector<int> elem; long long sum;
Equation(vector<int> e, long long s) : elem(e), sum(s) {}
void clear(vector<long long>& P, int bottom) {
while (elem.back() > bottom) { // elem[0] should not be less than bottom, so no need to check elem.empty();
sum -= P[elem.back()];
elem.pop_back();
}
}
};
Equation modified_transaction(long long M) {
pair<vector<int>, long long> raw = transaction(M);
return {raw.first, M - raw.second};
}
void buy_souvenirs(int N, long long P0) {
vector<long long> P(N, 0);
vector<int> kpi(N); // track how many of each type has been bought
for (int i = 0; i < N; i++) kpi[i] = i;
stack<Equation> S; // store info
int bottom = N - 1; // found P[i] forall i > bottom;
S.push({{0}, P0});
// find P
while (bottom) {
Equation u = S.top();
u.clear(P, bottom);
if (u.elem.size() == 1 && u.elem[0] == bottom) {
S.pop();
P[bottom] = u.sum;
bottom--;
} else {
long long amount = (u.sum - 1)/u.elem.size();
Equation next = modified_transaction(amount);
for (auto i: next.elem) kpi[i]--;
S.push(next);
}
}
// clean up
for (int i = 0; i < N; i++) while (kpi[i]--) transaction(P[i]);
}
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