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: Wrong Answer)

    #include <iostream>
    #include <string>
    #include <set>  
    #include <algorithm>
    #include <vector>
    #include <cmath>
    #include <queue>
    #include <deque>
    #include <cstring>
    #include <cstdio>
    #include <map>
    #include <numeric>
    #include <cassert>
    #include <iomanip>
    #include <sstream>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(int)(b);++i)
#define REP(i,N) FOR(i,0,N)
#define FORD(i,b,a) for(int i=(int)(b)-1;i>=a;--i)
typedef long long LL;
typedef pair<int,int> PII;
const int INF=1e9+7;
#define st first
#define nd second
#define pb push_back
#define eb emplace_back
#define dprintf(...) printf(__VA_ARGS__)
const int maxn=1e5+10;
int a,b,c,x,y;
int ans=INF;
int main()
{
	scanf("%d %d %d %d %d",&a,&b,&c,&x,&y);
	REP(i,max(x,y))
	{
		int res=i*2*c+max(0,x-i)*a+max(0,y-i)*b;
		ans=min(res,ans); 
	}
	printf("%d\n",ans);
	return 0;
}