Problem:
Score : 300 points

Problem Statement

"Pizza At", a fast food chain, offers three kinds of pizza: "A-pizza", "B-pizza" and "AB-pizza". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are A yen, B yen and C yen (yen is the currency of Japan), respectively.

Nakahashi needs to prepare X A-pizzas and Y B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas.

Constraints

1 ≤ A, B, C ≤ 5000

1 ≤ X, Y ≤ 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C X Y

Output

Print the minimum amount of money required to prepare X A-pizzas and Y B-pizzas.

Sample Input 1

1500 2000 1600 3 2

Sample Output 1

7900

It is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza.

Sample Input 2

1500 2000 1900 3 2

Sample Output 2

8500

It is optimal to directly buy three A-pizzas and two B-pizzas.

Sample Input 3

1500 2000 500 90000 100000

Sample Output 3

100000000

It is optimal to buy 200000 AB-pizzas and rearrange them into 100000 A-pizzas and 100000 B-pizzas. We will have 10000 more A-pizzas than necessary, but that is fine.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
    #include <algorithm>
    #include <vector>
    #include <map>
    #include <string>
    #include <cmath>
    #include <iomanip>
    #include <numeric>
     
    using namespace std;
     
    #define FOR(i, a, b) for (int i = (a); i < (b); i++)
    #define REP(i, n) FOR(i, 0, n)
    #define SORT(c) sort((c).begin(), (c).end())
    #define INF (ll)1e18
    #define MOD (ll)1e9 + 7
     
    typedef long long ll;
    typedef pair<int, int> P;
    typedef vector<int> V;
    typedef map<int, int> M;
    int main()
    {
        int a,b,c,x,y;
        cin>>a>>b>>c>>x>>y;
        int m=(int)1e9;
        for(int i=0;i<100001;i++){
            m=min(m,i*2*c+a*max(0,x-i)+b*max(0,y-i));
        }
        cout<<m<<endl;
        return 0;
    }