#include "festival.h"
#include <bits/stdc++.h>
using namespace std;
bool comp(array<long long,3>&a, array<long long,3>&b){
if(a[0]*a[1]*b[1]+b[0]*b[1]==b[0]*a[1]*b[1]+a[0]*a[1]){
return a[0]<b[0];
}
return a[0]*a[1]*b[1]+b[0]*b[1]<b[0]*a[1]*b[1]+a[0]*a[1];
}
vector<int> max_coupons(int A, vector<int> P, vector<int> T) {
int n = P.size();
array<long long,3>arr[n];
for(int i = 0;i<n;i++){
arr[i]={P[i],T[i],i};
}
sort(arr,arr+n,comp);
long long dp[n][n+1];
int par[n][n+1];
//j is 1 indexed.
const long long inf = 1e15;
for(int i = 0;i<n;i++){
fill(dp[i],dp[i]+n+1,-inf);
fill(par[i],par[i]+n+1,-1);
}
dp[0][0]=A;
dp[0][1]=(A-arr[0][0])*arr[0][1];
par[0][1]=0;
for(int i = 1;i<n;i++){
dp[i][0]=dp[i-1][0];
for(int j = 1;j<=n;j++){
dp[i][j]=max(dp[i-1][j],(dp[i-1][j-1]-arr[i][0])*arr[i][1]);
if(dp[i-1][j]>(dp[i-1][j-1]-arr[i][0])*arr[i][1]){
par[i][j]=par[i-1][j];
}
else{
par[i][j]=i;
}
dp[i][j]=min(dp[i][j],inf);
}
}
vector<int>ans;
int mx = 0;
for(int i = 0;i<=n;i++){
if(dp[n-1][i]>=0){
mx=i;
}
}
int curp = par[n-1][mx];
while(curp!=-1){
ans.push_back(curp);
mx--;
if(curp==0){
break;
}
curp=par[curp-1][mx];
}
reverse(ans.begin(),ans.end());
return ans;
}
