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())
while t>0:
	t-=1
	x,y = map(int,input().split())
	a,b = map(int,input().split())
	cost=0
	'''while x!=0 or y!=0:
		if x<0 and y<0:
			x+=1
			y+=1
			cost+=b
		elif x>0 and y>0:
			x-=1
			y-=1
			cost+=b
		elif x<0 and y>0:
			x+=1
			y-=1
			cost+=2*a
		elif x>0 and y<0:
			x-=1
			y+=1
			cost+=2*a 
		elif x==0:
			if y<0:
				y+=1
				cost+=a
			elif y>0:
				y-=1
				cost+=a
		elif y==0:
			if x<0:
				x+=1
				cost+=a
			elif x>0:
				x-=1
				cost+=a
	'''
	while x!=0 or y!=0:
		if x<0 and y<0:
			m = max(x,y)
			if m!=0:
				x+=abs(m)
				y+=abs(m)
				if cost+abs(m)*b < cost+abs(m)*2*a:
					cost+=abs(m)*b
				else:
					cost+=abs(m)*2*a
		elif x>0 and y>0:
			m = min(x,y)
			if m!=0:
				x-=abs(m)
				y-=abs(m)
				if cost+abs(m)*b < cost+abs(m)*2*a:
					cost+=abs(m)*b
				else:
					cost+=abs(m)*2*a
		elif (x>=0 and y<=0) or (x<=0 and y>=0):
			cost+=abs(x)*a+abs(y)*a
			x=0
			y=0



	print(cost)
