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.
def main(x,y,a,b):

	s1 = x*a + y*a
	s2 = (max(x, y) - min(x, y)) * a + min(x,y) * b
	return min(s1, s2)
	# min_price = 0
	# max_price = 0
	# min_i = 0
	# if a>b:
	# 	min_price = b
	# 	max_price = a
	# 	min_i = 1
	# else:
	# 	min_price = a
	# 	max_price = b
	# 	min_i = 0

	# c_1 = 0
	# c_2 = 0
	# max_v = 0
	# min_v = 0
	# if x>y:
	# 	max_v = x
	# 	min_v = y
	# else:
	# 	max_v = y
	# 	min_v = x


	# # while max_v != min_v:
	# # 	if max_v>0:
	# # 		max_v -= 1
	# # 	else:
	# # 		max_v += 1
	# # 	if min_i == 0:
	# # 		c_1 += 1
	# # 	else:
	# # 		c_2 += 1

	# difs = (max_v - min_v)

	# return difs*min_price + (abs(min_v - 0) * max_price)

	# # if min_i == 0:
	# # 	c_1 += 1
	# # else:
	# # 	c_2 += 1
	
	# # c_2 = min_v - 0


	# # return c_1*a + c_2*b



if __name__ == '__main__':
	t = int(input())

	for i in range(t):
		x,y = list(map(int,input().split()))
		a,b = list(map(int,input().split()))
		print(main(x,y,a,b))



