CF2119A Add or XOR

[r-906 & IA AI - Psychologic Disco](https://www.youtube.com/watch?v=NMiQmumW0nI) You are given two non-negative integers $ a, b $ . You can apply two types of operations on $ a $ any number of times and in any order: - $ a \gets a + 1 $ . The cost of this operation is $ x $ ; - $ a \gets a \oplus 1 $ , where $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). The cost of this operation is $ y $ . Now you are asked to make $ a = b $ . If it's possible, output the minimum cost; otherwise, report it.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The only line of each test case contains four integers $ a, b, x, y $ ( $ 1 \le a, b \le 100, 1 \le x, y \le 10^7 $ ) — the two integers given to you and the respective costs of two types of operations.

For each test case, output an integer — the minimum cost to make $ a = b $ , or $ -1 $ if it is impossible.

In the first test case, the optimal strategy is to apply $ a \gets a + 1 $ three times. The total cost is $ 1+1+1=3 $ . In the second test case, the optimal strategy is to apply $ a \gets a + 1 $ , $ a \gets a \oplus 1 $ , $ a \gets a + 1 $ , $ a \gets a \oplus 1 $ in order. The total cost is $ 2+1+2+1=6 $ . In the fifth test case, it can be proved that there isn't a way to make $ a = b $ .