CF2108B SUMdamental Decomposition

On a recent birthday, your best friend Maurice gave you a pair of numbers $ n $ and $ x $ , and asked you to construct an array of positive numbers $ a $ of length $ n $ such that $ a_1 \oplus a_2 \oplus \cdots \oplus a_n = x $ $ ^{\text{∗}} $ . This task seemed too simple to you, and therefore you decided to give Maurice a return gift by constructing an array among all such arrays that has the smallest sum of its elements. You immediately thought of a suitable array; however, since writing it down turned out to be too time-consuming, Maurice will have to settle for just the sum of its elements. $ ^{\text{∗}} $ $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

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. Each test case consists of a single line containing a pair of numbers $ n $ and $ x $ ( $ 1 \le n \le 10^9, \; 0 \le x \le 10^9 $ ) — the numbers given to you by Maurice.

For each test case, output your gift to Maurice — the sum of the elements of the array that satisfies all the described properties. If a suitable array does not exist, output $ -1 $ .

In the first test case, one of the suitable arrays is $ [2, 3] $ . It can be shown that it is impossible to achieve a smaller sum of array elements. In the second case, one of the suitable arrays is $ [1, 3, 4] $ . It can also be shown that this is the optimal amount.