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.
# Importing Modules
from collections import *
from itertools import *
from functools import *
import sys
import os
import time
# ~ import numpy as np


# Debugging and Timer Flags
timer = False
debug = False

# ---------- Helper Functions -----------
def timeit(method):
    def wrapper(*args, **kwargs):
        mname = method.__name__
        if debug:
            print("{}(args:{}, kwargs:{})".format(mname, args,kwargs))
        if timer:
            ts = time.time()
        result = method(*args, **kwargs)
        if timer:
            te = time.time()
            print('%r  %2.2f ms'% (mname, (te-ts) * 1000))
        return result
    return wrapper
# ----------------------------------------




@timeit
def main():
    t = int(input())
    for _ in range(t):
        x,y = map(int,input().split())
        a,b = map(int,input().split())
        if abs(x)<abs(y):
            min_val = x
            max_val = y
        else:
            min_val = y
            max_val = x
        c = abs(min_val) * b + (max_val-min_val)*a
        d = abs(x)*a + abs(y)*a

        print(min(c,d))



if __name__=="__main__":
    main()
