CF1342A Road To Zero

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.

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.

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.