Road To Zero
Description
You are given two integers $x$ and $y$. You can perform two types of operations:
- 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:
- $x = 0$, $y = 6$;
- $x = 0$, $y = 8$;
- $x = -1$, $y = 7$;
- $x = 1$, $y = 7$.
- 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.
The first line contains one integer $t$ ($1 \le t \le 100$) — the number of testcases.
The first line of each test case contains two integers $x$ and $y$ ($0 \le x, y \le 10^9$).
The second line of each test case contains two integers $a$ and $b$ ($1 \le a, b \le 10^9$).
For each test case print one integer — the minimum amount of dollars you have to spend.
Input
The first line contains one integer $t$ ($1 \le t \le 100$) — the number of testcases.
The first line of each test case contains two integers $x$ and $y$ ($0 \le x, y \le 10^9$).
The second line of each test case contains two integers $a$ and $b$ ($1 \le a, b \le 10^9$).
Output
For each test case print one integer — the minimum amount of dollars you have to spend.
Samples
2
1 3
391 555
0 0
9 4
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.