#D5921. Road To Zero
Road To Zero
Road To Zero
You are given two integers x and y. You can perform two types of operations:
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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.
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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.
inputFormat
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).
outputFormat
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.
样例
2
1 3
391 555
0 0
9 4
1337
0