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.
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
import sys
# sys.stdin=open('input.txt','r')
# sys.stdout=open('output.txt','w')
input=sys.stdin.readline
# sys.setrecursionlimit(300010)
MOD = 1000000007
MOD2 = 998244353
ii = lambda: int(input().strip('\n'))
si = lambda: input().strip('\n')
dgl = lambda: list(map(int,input().strip('\n')))
f = lambda: map(int, input().strip('\n').split())
il = lambda: list(map(int, input().strip('\n').split()))
ls = lambda: list(input().strip('\n'))
let = 'abcdefghijklmnopqrstuvwxyz'
for _ in range(ii()):
    x,y=f()
    a,b=f()
    ans=(abs(x)+abs(y))*a
    if x*y>0:
        x=abs(x)
        y=abs(y)
        ans=min(min(x,y)*b+(max(x,y)-min(x,y))*a,ans)
    print(ans)