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 JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict'

function main(s) {
  s = s.split('\n')[0].split(' ').map(n => Number(n));

  const A = s[0];
  const B = s[1];
  const C = s[2];
  const X = s[3];
  const Y = s[4];
  const min = Math.min(X, Y);

  // AとBをそれぞれ買う
  const case1 = A * X + B * Y

  // ABセットで可能な限り組み替えて、残りをそれぞれ買う
  const case2 = (2 * C * min) + ((X - min) * A) + ((Y - min) * B)

  // 全てABセットで組み替える
  const case3 = 2 * C * Math.max(X, Y);

  const answer = Math.min(...[case1, case2, case3]);
  console.log(answer);
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));