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.
test_case = int(input())

road_list=[]
dollars = []
cost1 = 0
cost2=0
for i in range(test_case):
	x,y = input().split()
	road_list.append(int(x))
	road_list.append(int(y))

	a,b = input().split()
	dollars.append(int(a))
	dollars.append(int(b))
index=0
while(index<len(road_list)):

	x = road_list[index]
	y = road_list[index+1]
	a = dollars[index]
	b = dollars[index+1]

	if (x == y and x == 0):
		print(0)
	elif(x==y and x!=0):
		cost1 = x*b
		cost2 = ((x*a)+(y*a))
		if cost1>cost2:
			print(cost2)
		else:
			print(cost1)

	elif(x!=y and x>y):
		cost2 = ((x*a)+(y*a))
		cost1 = y * b
		x = x-y
		cost1 += (x*a)

		if cost1 > cost2:
			print(cost2)
		else:
			print(cost1)


	elif(x!=y and y>x):
		cost2 = ((x*a)+(y*a))
		cost1 = x * b
		y = y-x
		cost1 += (y*a)


		if cost1>cost2:
			print(cost2)
		else:
			print(cost1)
	cost1= 0
	cost2= 0
	index += 2