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.
#8:47
MOD=10**9+7
INT_MAX=10**20+7
def INPUT():return list(int(i) for i in input().split())
def LIST_1D_ARRAY(n):return [0 for _ in range(n)]
def LIST_2D_ARRAY(m,n):return [[0 for _ in range(n)]for _ in range(m)]
def power(a,x):
    res=1
    while(x>0):
        if x&1:
            res=(res*a)%MOD
        a=(a*a)%MOD
        x//=2
    return res%MOD
def NCR_MOD(n,r):
    num=1
    for i in range(n,n-r,-1):num=(num*i)%MOD
    for j in range(1,r+1):num=(num*power(j,MOD-2))%MOD
    return num
#################################################################################
def calc(x,y,a,b):
    ans=0
    ans+=(max(x,y)-min(x,y))*a
    ans+=min(x,y)*(min(2*a,b))
    print(ans)
for _ in range(int(input())):
    x,y=INPUT()
    a,b=INPUT()
    calc(x,y,a,b)
