CF2162C Beautiful XOR

You are given two integers $ a $ and $ b $ . You are allowed to perform the following operation any number of times (including zero): - choose any integer $ x $ such that $ 0 \le x \le a $ (the current value of $ a $ , not initial), - set $ a := a \oplus x $ . Here, $ \oplus $ represents the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operator. After performing a sequence of operations, you want the value of $ a $ to become exactly $ b $ . Find a sequence of at most $ 100 $ operations (values of $ x $ used in each operation) that transforms $ a $ into $ b $ , or report that it is impossible. Note that you are not required to find the minimum number of operations, but any valid sequence of at most $ 100 $ operations.

The first line of input contains a single integer $ t $ ( $ 1 \le t \le 1000 $ ) — the number of test cases. Each test case contains two integers $ a $ and $ b $ ( $ 1 \le a, b \le 10^9 $ ).

For each test case, if it is impossible to obtain $ b $ from $ a $ using the allowed operations, print a single line containing $ -1 $ . Otherwise, on the first line print a single integer $ k $ ( $ 0 \le k \le 100 $ ) — the number of operations. On the second line print $ k $ integers ( $ x_1, x_2, \dots , x_k $ ) — the chosen values of $ x $ in the order you apply them. If there are multiple valid sequences, you may print any one of them.

For the first test case, - choose $ x = 7 $ , now $ a $ becomes equal to $ 9 \oplus 7 = 14 $ . - choose $ x = 8 $ , now $ a $ becomes equal to $ 14 \oplus 8 = 6 $ . Thus, we can make $ a = b $ .For the fourth test case, choosing $ x = 5 $ makes $ a = b $ .