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.
z=input
mod = 10**9 + 7
from collections import *
from queue import *
from sys import *
from collections import *
from math import *
from heapq import *
from itertools import *
from bisect import *
from collections import Counter as cc
from math import factorial as f
def lcd(xnum1,xnum2):
    return (xnum1*xnum2//gcd(xnum1,xnum2))

################################################################################

"""

n=int(z())

for _ in range(int(z())):

x=int(z())

l=list(map(int,z().split()))

n=int(z())

l=sorted(list(map(int,z().split())))[::-1]

a,b=map(int,z().split())

l=set(map(int,z().split()))

led=(6,2,5,5,4,5,6,3,7,6)

vowel={'a':0,'e':0,'i':0,'o':0,'u':0}

color-4=["G", "GB", "YGB", "YGBI", "OYGBI" ,"OYGBIV",'ROYGBIV' ]

"""

###########################---START-CODING---###############################################


for _ in range(int(z())):
    x,y=sorted(list(map(int,z().split())))
    a,b=map(int,z().split())
    i=0
    t=a*2
    t2=b
    if t<=t2:
        p1=a*x
        p2=a*y
        p3=0

    else:
        p1=x*b
        p2=(y-x)*a
        p3=0

        
    print(p1+p2+p3)
        
        
    
        
        
        
    
    
    
        
        
        
        
        
    
            
            
            
        
        
        
    
        
            
            
            













    
