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):
    str = input()
    x, y = str.split()
    x = int(x)
    y = int(y)
    str = input()
    a, b = str.split()
    a = int(a)
    b = int(b)
    
    cost = 0
    
    # Check 2a < b
    if (a*2 < b):
        b = a*2
    
    # Both higher than 0
    if (x > 0 and y > 0):
        # Switch pos if needed
        if (x > y):
            n = x
            x = y
            y = n
        
        cost += b*x
        y -= x
        x -= x
        
        cost += a*y
        print(cost)
    
    # Both lower than 0
    elif (x < 0 and y < 0):
        # Switch pos if needed
        if (x < y):
            n = x
            x = y
            y = n
        
        cost -= b*x
        y -= x
        x -= x
        
        cost -= a*y
        print(cost)
    
    # Either one is positive and negative
    else:
        ttl = abs(x) + abs(y)
        cost += a*ttl
        print(cost)