#include <bits/stdc++.h>
using namespace std;
static inline long long sat_add(long long a, long long b, long long CAP) {
__int128 v = (__int128)a + (__int128)b;
if (v > CAP) return CAP;
if (v < -(__int128)CAP) return -CAP; // not really needed here
return (long long)v;
}
static inline long long sat_sub(long long a, long long b, long long CAP) {
__int128 v = (__int128)a - (__int128)b;
if (v > CAP) return CAP;
if (v < -(__int128)CAP) return -CAP;
return (long long)v;
}
static inline long long sat_mul(long long a, long long b, long long CAP) {
__int128 v = (__int128)a * (__int128)b;
if (v > CAP) return CAP;
if (v < -(__int128)CAP) return -CAP;
return (long long)v;
}
// Safe check for: token * (t-1) >= p * t with saturation not needed for correctness
static inline bool feasible_prefix(long long token, int p, int t) {
__int128 L = (__int128)token * (t - 1);
__int128 R = (__int128)p * t;
return L >= R;
}
std::vector<int> max_coupons(int A, std::vector<int> P, std::vector<int> T) {
int n = (int)P.size();
// coeff[t] = 12*t/(t-1) for t in {2,3,4}
const int coeff[5] = {0, 0, 24, 18, 16};
// ---------- split coupons ----------
vector<pair<long long,int>> cheap; // (price, idx) for T=1
struct Booster {
long long key; // p * coeff[t] (fits in 64-bit for p<=1e9)
int p;
int t;
int idx;
};
vector<Booster> boosters;
cheap.reserve(n);
boosters.reserve(n);
long long SUM_CHEAP = 0;
int MAXP = 0;
for (int i = 0; i < n; i++) {
int ti = T[i];
int pi = P[i];
MAXP = max(MAXP, pi);
if (ti == 1) {
cheap.push_back({(long long)pi, i});
SUM_CHEAP += (long long)pi;
} else {
long long key = 1LL * pi * coeff[ti];
boosters.push_back({key, pi, ti, i});
}
}
// Choose a saturation cap large enough that exact values above it don't matter.
// K=61 from the algorithm; extra slack is fine.
const int K = 61;
long long CAP = SUM_CHEAP;
CAP = sat_add(CAP, sat_mul(4LL * MAXP, (long long)(K + 5), (long long)9e18), (long long)9e18);
CAP = sat_add(CAP, A, (long long)9e18);
// ---------- sort ----------
sort(cheap.begin(), cheap.end(),
[](const auto& a, const auto& b){ return a.first < b.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;
});
// cheap prefix sums (64-bit safe)
vector<long long> cheap_psum(cheap.size() + 1, 0);
vector<int> cheap_idx(cheap.size());
for (size_t i = 0; i < cheap.size(); i++) {
cheap_psum[i + 1] = cheap_psum[i] + cheap[i].first;
cheap_idx[i] = cheap[i].second;
}
auto cheap_cnt_from_token = [&](long long tok) -> int {
// If tok is saturated beyond SUM_CHEAP, we can buy all cheap.
if (tok >= SUM_CHEAP) return (int)cheap.size();
auto it = upper_bound(cheap_psum.begin(), cheap_psum.end(), tok);
return int(it - cheap_psum.begin()) - 1;
};
// ---------- take all non-decreasing boosters ----------
long long token = min<long long>(A, CAP);
vector<int> prefix_ids;
prefix_ids.reserve(boosters.size());
int i = 0, m = (int)boosters.size();
while (i < m) {
const auto &b = boosters[i];
if (feasible_prefix(token, b.p, b.t)) {
prefix_ids.push_back(b.idx);
// token = (token - p) * t with saturation
token = sat_mul(sat_sub(token, b.p, CAP), b.t, CAP);
i++;
} else break;
}
// ---------- hard suffix DP ----------
int h_len = m - i;
vector<long long> dp(K + 1, -1);
dp[0] = token;
vector<vector<uint8_t>> parent(h_len, vector<uint8_t>(K + 1, 0));
for (int j = 0; j < h_len; j++) {
const auto &b = boosters[i + j];
int max_c = min(j + 1, K);
for (int c = max_c; c >= 1; c--) {
long long prev = dp[c - 1];
if (prev < 0) continue;
if (prev >= b.p) {
long long cand = sat_mul(sat_sub(prev, b.p, CAP), b.t, CAP);
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;
int cheap_cnt = cheap_cnt_from_token(cur);
int total = i + c + cheap_cnt;
if (total > best_total) {
best_total = total;
best_c = c;
best_token = cur;
}
}
// ---------- reconstruct chosen hard subset ----------
vector<int> chosen_hard_pos;
chosen_hard_pos.reserve(best_c);
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 final answer ----------
vector<int> answer;
answer.reserve(prefix_ids.size() + chosen_hard_pos.size() + cheap.size());
for (int id : prefix_ids) answer.push_back(id);
for (int pos : chosen_hard_pos) answer.push_back(boosters[i + pos].idx);
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;
}
