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"
)

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
	
	A := ScanInt(scanner)
	B := ScanInt(scanner)
	C := ScanInt(scanner)
	X := ScanInt(scanner)
	Y := ScanInt(scanner)
	
	if (A + B < 2 * C) {
	    fmt.Println(A * X + B * Y)
	} else {
	    max := Max(X, Y)
	    min := Min(X, Y)
	    
	    ans := 2 * C * min
	    
	    max -= min
	    if max > 0 {
	        if min == A {
	            if B < 2 * C {
	                ans += B * max
	            } else {
	                ans += 2 * C * max
	            }
	        } else {
	            if A < 2 * C {
	                ans += A * max
	            } else {
	                ans += 2 * C * max
	            }
	        }
	    }
	    fmt.Println(ans)
	}
}

func ScanInt(scanner *bufio.Scanner) int {
	scanner.Scan()
	i, e := strconv.Atoi(scanner.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func ScanFloat64(scanner *bufio.Scanner) float64 {
	scanner.Scan()
	f, e := strconv.ParseFloat(scanner.Text(), 64)
	if e != nil {
		panic(e)
	}
	return f
}

func ScanText(scanner *bufio.Scanner) string {
	scanner.Scan()
	return scanner.Text()
}

func Max(a, b int) int {
	if a < b {
		return b
	}
	return a
}

func Min(a, b int) int {
	if a > b {
		return b
	}
	return a
}

func Abs(a int) int {
	if a < 0 {
		a *= -1
	}
	return a
}