#include <bits/stdc++.h>
using namespace std;
// Translate of the given Python function.
// Returns the list of chosen coupon original indices (0-based), in the same order
// as the Python code builds `answer`.
vector<int> max_coupons(long long A, const vector<long long>& P, const vector<int>& T) {
int n = (int)P.size();
// ---------- split coupons ----------
vector<pair<long long,int>> cheap; // (price, original_index) for T==1
// boosters: (weight_key, price, t, original_index)
struct Booster {
long long key;
long long p;
int t;
int idx;
};
vector<Booster> boosters;
// coeff = 12 * T / (T-1) for T in {2,3,4} -> {24,18,16}
unordered_map<int, long long> coeff;
coeff[2] = 24;
coeff[3] = 18;
coeff[4] = 16;
long long max_price = 0;
for (int i = 0; i < n; i++) {
int ti = T[i];
long long pi = P[i];
if (ti == 1) {
cheap.push_back({pi, i});
} else {
long long key = pi * coeff[ti];
boosters.push_back({key, pi, ti, i});
max_price = max(max_price, pi);
}
}
// ---------- sort ----------
sort(cheap.begin(), cheap.end(), [](auto &a, 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; // tie-break by price
});
vector<long long> cheap_prices;
vector<int> cheap_idx;
cheap_prices.reserve(cheap.size());
cheap_idx.reserve(cheap.size());
for (auto &cp : cheap) {
cheap_prices.push_back(cp.first);
cheap_idx.push_back(cp.second);
}
// prefix sums of cheap prices
// cheap_psum[k] = sum of first k cheap prices, cheap_psum[0]=0
vector<long long> cheap_psum;
cheap_psum.reserve(cheap_prices.size() + 1);
cheap_psum.push_back(0);
for (long long p : cheap_prices) {
cheap_psum.push_back(cheap_psum.back() + p);
}
auto bisect_right = [&](const vector<long long>& arr, long long x) -> int {
// returns first index > x
return (int)(upper_bound(arr.begin(), arr.end(), x) - arr.begin());
};
// ---------- 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;
int t = b.t;
int idx = b.idx;
// Python: if token * (t - 1) >= p * t
// Use __int128 to avoid overflow.
__int128 L = (__int128)token * (t - 1);
__int128 R = (__int128)p * t;
if (L >= R) {
prefix_ids.push_back(idx);
// token = (token - p) * t
token = (token - p) * (long long)t;
i++;
} else {
break;
}
}
// ---------- hard suffix ----------
vector<Booster> hard;
for (int k = i; k < m; k++) hard.push_back(boosters[k]);
int h_len = (int)hard.size();
const int K = 61; // safe upper bound per original code
vector<long long> dp(K + 1, -1);
dp[0] = token;
// predecessor table: parent[j][c] = 1 iff hard[j] used for dp[c]
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;
int 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) * (long long)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];
for (int c = 0; c <= min(K, h_len); c++) {
long long cur = dp[c];
if (cur < 0) continue;
// cheap_cnt = bisect_right(cheap_psum, cur) - 1
int cheap_cnt = bisect_right(cheap_psum, cur) - 1;
int total = i + c + cheap_cnt;
if (total > best_total) {
best_total = total;
best_c = c;
best_token = cur;
}
}
// ---------- reconstruct the chosen hard subset ----------
vector<int> chosen_hard; // indices (within hard) chosen by DP
int need = best_c;
for (int j = h_len - 1; j >= 0; j--) {
if (need == 0) break;
if (parent[j][need]) {
chosen_hard.push_back(j);
need--;
}
}
reverse(chosen_hard.begin(), chosen_hard.end()); // keep original order
// ---------- build the final answer ----------
vector<int> answer;
// prefix boosters
answer.insert(answer.end(), prefix_ids.begin(), prefix_ids.end());
// hard boosters selected by DP
// Note: same as python, we just append indices; token already best_token
token = best_token;
for (int j : chosen_hard) {
answer.push_back(hard[j].idx);
}
// cheap coupons as many as we can afford now
int cheap_cnt_final = bisect_right(cheap_psum, token) - 1;
for (int k = 0; k < cheap_cnt_final; k++) {
answer.push_back(cheap_idx[k]);
}
return answer;
}
