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.
#!/usr/bin/python3

# Codeforces - Educational Round 86
# Problem A - 


def read_int():
	n = int(input())
	return n


def read_ints():
	ints = [int(x) for x in input().split(" ")]
	return ints
	

#---

def solve(x,y,a,b):
	n = 0
	while True:
		if x == 0 and y == 0:
			break
			
		if x == 0:
			n += y * a
			y = 0
				
		elif y == 0:
			n += x * a
			x = 0
		
		else:		
			if b < a*2:
				mn = min(x, y)
				n += b * mn
					
				x -= mn
				y -= mn
			
			else:
				n += (x+y) * a
				x = 0
				y = 0
				
		#print ("{} {}".format(x,y))
		
	return n


# Main
t = read_int()
for case in range(t):
	x, y = read_ints()
	a, b = read_ints()
	
	sol = solve(x, y, a, b)
	
	print (sol)
