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.
# -*- coding: utf-8 -*-
"""
Created on Sat May 23 17:34:20 2020

@author: user
"""
import sys
input = sys.stdin.readline
output=sys.stdout

def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))

def solve(x,y,a,b):
    if(2*a<=b):
        #use a as much as possible
        res=(x+y)*a
    else:
        #use b upto one becomes 0 then a
        if(x==y):
            res=x*b
        elif(x>y):
            res=(y*b)+((x-y)*a)
        elif(x<y):
            res=(x*b)+((y-x)*a)
    print(res)
    
n=inp()
for i in range(n):
    my_list1=inlt()
    my_list2=inlt()
    a1=my_list1[0]
    a2=my_list1[1]
    b1=my_list2[0]
    b2=my_list2[1]
    solve(a1,a2,b1,b2)