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 (GCC 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>


int main(void){

    int Aprice,Bprice,Cprice;
    int numA,numB;

    scanf("%d %d %d %d %d",&Aprice,&Bprice,&Cprice,&numA,&numB);

    long ans=5000000000;
    int numMAX=0;
    if(numA>numB) numMAX=numA;
    else numMAX=numB;

    long price;

    for(int i=0;i<=numMAX;i++){
        if(numA>=i && numB>=i) price=Aprice*(numA-i)+Bprice*(numB-i)+Cprice*2*i;
        else if(numA>=i && numB<i) price=Aprice*(numA-i)+Cprice*2*i;
        else if(numA<i && numB>=i) price=Bprice*(numB-i)+Cprice*2*i;
        
        if(price<ans) ans=price;
    }

    printf("%ld\n",ans);
    
    return 0;
}