#include <bits/stdc++.h>
using namespace std;
std::vector<int> max_coupons(int A, std::vector<int> P, std::vector<int> T) {
int n = (int)P.size();
// ---------- split coupons ----------
vector<pair<long long,int>> cheap; // (price, original_index) for T=1
struct Booster {
long long key; // pi * coeff[ti]
int p;
int t;
int idx;
};
vector<Booster> boosters; // for T>1
// coeff = 12*T/(T-1) for T in {2,3,4}
unordered_map<int,int> coeff{{2,24},{3,18},{4,16}};
int max_price = 0;
for (int i = 0; i < n; i++) {
int ti = T[i];
int pi = P[i];
if (ti == 1) {
cheap.push_back({pi, i});
} else {
long long key = 1LL * pi * coeff[ti];
boosters.push_back({key, pi, ti, i});
max_price = max(max_price, pi);
}
}
// ---------- sort ----------
sort(cheap.begin(), cheap.end(),
[](const auto& a, const auto& b){ return a.first < b.first; }); // cheapest first
sort(boosters.begin(), boosters.end(),
[](const Booster& a, const Booster& b){
if (a.key != b.key) return a.key < b.key;
return a.p < b.p;
});
vector<long long> cheap_prices;
vector<int> cheap_idx;
cheap_prices.reserve(cheap.size());
cheap_idx.reserve(cheap.size());
for (auto &pr : cheap) {
cheap_prices.push_back(pr.first);
cheap_idx.push_back(pr.second);
}
// prefix sums of cheap prices
vector<long long> cheap_psum(cheap_prices.size() + 1, 0);
for (size_t i = 0; i < cheap_prices.size(); i++) {
cheap_psum[i + 1] = cheap_psum[i] + cheap_prices[i];
}
// ---------- take all non-decreasing boosters ----------
long long token = A;
vector<int> prefix_ids; // original indices of taken prefix boosters
int i = 0;
int m = (int)boosters.size();
while (i < m) {
const auto &b = boosters[i];
long long p = b.p;
long long t = b.t;
// token * (t-1) >= p * t
if (token * (t - 1) >= p * t) {
prefix_ids.push_back(b.idx);
token = (token - p) * t;
i++;
} else {
break;
}
}
// ---------- hard suffix ----------
vector<Booster> hard;
hard.reserve(m - i);
for (int j = i; j < m; j++) hard.push_back(boosters[j]);
int h_len = (int)hard.size();
const int K = 61; // safe upper bound
vector<long long> dp(K + 1, -1);
dp[0] = token;
// parent[j][c] = 1 iff hard[j] is used to achieve dp[c] at step j
vector<vector<uint8_t>> parent(h_len, vector<uint8_t>(K + 1, 0));
for (int j = 0; j < h_len; j++) {
long long p = hard[j].p;
long long t = hard[j].t;
int max_c = min(j + 1, K);
for (int c = max_c; c >= 1; c--) {
long long prev = dp[c - 1];
if (prev >= p) {
long long cand = (prev - p) * t;
if (cand > dp[c]) {
dp[c] = cand;
parent[j][c] = 1;
}
}
}
}
// ---------- evaluate all possibilities ----------
int best_total = -1;
int best_c = 0;
long long best_token = dp[0];
auto cheap_cnt_from_token = [&](long long tok) -> int {
// number of cheap items affordable = max k s.t. cheap_psum[k] <= tok
auto it = upper_bound(cheap_psum.begin(), cheap_psum.end(), tok);
return int(it - cheap_psum.begin()) - 1;
};
for (int c = 0; c <= min(K, h_len); c++) {
long long cur = dp[c];
if (cur < 0) continue;
int cheap_cnt = cheap_cnt_from_token(cur);
int total = i + c + cheap_cnt; // i boosters from prefix + c from hard + cheap_cnt
if (total > best_total) {
best_total = total;
best_c = c;
best_token = cur;
}
}
// ---------- reconstruct the chosen hard subset ----------
vector<int> chosen_hard_pos;
int need = best_c;
for (int j = h_len - 1; j >= 0 && need > 0; j--) {
if (parent[j][need]) {
chosen_hard_pos.push_back(j);
need--;
}
}
reverse(chosen_hard_pos.begin(), chosen_hard_pos.end());
// ---------- build the final answer ----------
vector<int> answer;
answer.reserve(prefix_ids.size() + chosen_hard_pos.size() + cheap_idx.size());
// prefix boosters
for (int id : prefix_ids) answer.push_back(id);
// selected hard boosters (append original indices)
for (int pos : chosen_hard_pos) {
answer.push_back(hard[pos].idx);
}
// cheap coupons (as many as affordable with best_token)
int cheap_cnt_final = cheap_cnt_from_token(best_token);
for (int k = 0; k < cheap_cnt_final; k++) {
answer.push_back(cheap_idx[k]);
}
return answer;
}
