You are given two integers x and y. You can perform two types of operations: 

  1. Pay a dollars and increase or decrease any of these integers by 1. For example, if x = 0 and y = 7 there are four possible outcomes after this operation: 
    * x = 0, y = 6; 
    * x = 0, y = 8; 
    * x = -1, y = 7; 
    * x = 1, y = 7. 

  2. Pay b dollars and increase or decrease both integers by 1. For example, if x = 0 and y = 7 there are two possible outcomes after this operation: 
    * x = -1, y = 6; 
    * x = 1, y = 8. 



Your goal is to make both given integers equal zero simultaneously, i.e. x = y = 0. There are no other requirements. In particular, it is possible to move from x=1, y=0 to x=y=0.

Calculate the minimum amount of dollars you have to spend on it.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of testcases.

The first line of each test case contains two integers x and y (0 ≤ x, y ≤ 10^9).

The second line of each test case contains two integers a and b (1 ≤ a, b ≤ 10^9).

Output

For each test case print one integer — the minimum amount of dollars you have to spend.

Example

Input


2
1 3
391 555
0 0
9 4


Output


1337
0

Note

In the first test case you can perform the following sequence of operations: first, second, first. This way you spend 391 + 555 + 391 = 1337 dollars.

In the second test case both integers are equal to zero initially, so you dont' have to spend money.
t=int(input())
for i in range(t):
    l1=str.split(input()," ")
    l2=str.split(input()," ")
    x=int(l1[0])
    y=int(l1[1])
    a=int(l2[0])
    b=int(l2[1])
    if(b>=2*a):
        ans=abs(x)
        ans=abs(y)+ans
        ans=ans*a
        print(ans)
    else:
        if((a>0 and b<0) or (a<0 and b>0)):
            ans=abs(x)
            ans=abs(y)+ans
            ans=ans*a
            print(ans)
        else:
            x=abs(x)
            y=abs(y)
            if(x>y):
                ans = y*b
                x=x-y
                ans = ans + x*a
                print(ans)
            else:
                ans = x*b
                y=y-x
                ans = ans + y*a
                print(ans)
            
            
    
