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.
import sys
input = sys.stdin.readline

############ Input Functions ################

# Take integer input
def inp():
    return(int(input()))
# Take list input
def inlt():
    return(list(map(int, input().split())))
# Take string as list of characters
def insr():
    s = input()
    return(s[:len(s) - 1])
# Take space separated integer variable inputs
def invr():
    return(map(int, input().split()))

################ Solution ##################
def solve(dim, t):
    x, y = dim
    a, b = t

    effort = abs(x) + abs(y)

    if 2*a<=b:
        cost = effort * a
        print(cost)
    else:
        cost = 0
        if (x < 0 and y < 0) or (x > 0 and y > 0):
            cost += min(abs(x), abs(y)) * b
            effort -= 2 * min(abs(x), abs(y))
        cost += effort * a
        print(cost)
            

################ Read Input ################

T = inp()
dims = []
tests = []

for _ in range(T):

    # Read dimensions
    dims.append(inlt())
    # inp() 

    # Read data
    # tests.append(inp())
    tests.append(inlt())
    # tests.append(insr())
    # tests.append(invr())

for i in range(T):
    solve(dims[i], tests[i])
