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.
n = int(input())
x = []
y = []
a = []
b = []
mon_b = [0] * n
mon_a = [0] * n
for i in range(n):
    x_y = list(map(int, input().split()))
    x.append(x_y[0])
    y.append(x_y[1])
    ab = list(map(int, input().split()))
    a.append(ab[0])
    b.append(ab[1])
for i in range(n):
    if x[i] > y[i]:
        k = x[i] - y[i]
        mon_a[i] = k * a[i]
        x[i] = y[i]
    elif y[i] > x[i]:
        k = y[i] - x[i]
        mon_a[i] = k * a[i]
        y[i] = x[i]
    if x[i] * a[i] + y[i] * a[i] > b[i] * x[i]: 
        mon_b[i] = b[i] * x[i]
    else: 
        mon_b[i] = x[i] * a[i] + y[i] * a[i]   
        

for i in range(n):

    print(mon_a[i] + mon_b[i])