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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)

func main() {

	// input
	params := inputLineAsNumArray(5)
	pA := params[0]
	pB := params[1]
	pAB := params[2]
	rA := params[3]
	rB := params[4]

	var a, b, ab int
	//created
	cA := 0
	cB := 0

	sum := 0
	if pAB < (pA+pB)/2 {
		min := min(rA, rB)
		sum += min * 2 * pAB
		cA += min
		cB += min

		ab += min * 2
	}

	if 2*pAB < pA {
		toCreate := (rA - cA)
		sum += toCreate * 2 * pAB
		cA += toCreate
		cB += toCreate

		ab += toCreate * 2
	}

	if 2*pAB < pB {
		toCreate := (rB - cB)
		sum += toCreate * 2 * pAB
		cA += toCreate
		cB += toCreate

		ab += toCreate * 2
	}

	if (rA - cA) > 0 {
		toCreate := (rA - cA)
		sum += toCreate * pA

		a += toCreate
	}

	if (rB - cB) > 0 {

		toCreate := (rB - cB)
		sum += toCreate * pB

		b += toCreate
	}

	fmt.Println(sum)
}

func min(x, y int) int {
	if x <= y {
		return x
	} else {
		return y
	}
}

func max(x, y int) int {
	if x >= y {
		return x
	} else {
		return y
	}
}

func inputLineAsNumArray(length int) []int {

	line := strings.Split(readLine(), " ")
	var nums []int
	for i := 0; i < length; i++ {
		num, _ := strconv.Atoi(line[i])
		nums = append(nums, num)
	}
	return nums
}

func readLine() string {

	sc.Scan()
	return sc.Text()
}