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.
inp=input
li=list
iinp=lambda : int(inp())
ent=lambda : map(int,inp().split())
lient=lambda : [int(i) for i in inp().split()]
li0= lambda x: [0 for i in range(x)]
livalor=lambda valor,x: [valor for i in range(x)]
stent=lambda : [i for i in inp()]
filldp=lambda valor,x,y: [[valor for i in range(y)] for i in range(x)]
mi=min
ma=max

t=iinp()
for _ in range(t):
    x,y=ent()
    a,b=ent()
    if x==y==0: 
        print(0)
    elif x==y and x>0:
        print(mi(x*b,x*a*2))
    elif x==y and x<0:
        print(mi(x*b*-1,x*a*2*-1))
    elif x<0 and y>0:
        print(a*x*-1+a*y)
    elif x>0 and y<0:
        print(a*x+y*a*-1)
    else:
        if x<0: x=x*-1
        if y<0: y=y*-1

        tmp=ma(x,y)
        x=mi(x,y)
        y=tmp
        cont=a*(y-x)
        print(mi(cont+x*b,x*a+y*a))