Problem Statement

You are given positive integers $C$ and $X$ that are less than $2^{30}$.

Determine whether there exists a positive integer $n$ that satisfies all of the following conditions, and if it exists, find one such $n$.

• $1\le n < 2^{60}$
• $(n \oplus C) \bmod n=X$

Here, $n \oplus C$ denotes the bitwise $\mathrm{XOR}$ of $n$ and $C$.

You are given $T$ test cases, solve each of them.

What is bitwise $\mathrm{XOR}$? The bitwise $\mathrm{XOR}$ of non-negative integers $X$ and $Y$, $X \oplus Y$, is defined as follows: When $X \oplus Y$ is written in binary, the digit in the $2^k$ place ($k \geq 0$) is $1$ if exactly one of the digits in the $2^k$ place of $X$ and $Y$ written in binary is $1$, and $0$ otherwise. For example, $3 \oplus 5 = 6$ (in binary: $011 \oplus 101 = 110$).

Constraints

• $1\le T\le 2\times 10^5$
• $1\le C,X < 2^{30}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

C X

Output

Output the answers for each test case in order, separated by newlines.

For each test case, if there does not exist an $n$ that satisfies all conditions, print -1.

Otherwise, print $n$ that satisfies all conditions.

If there are multiple $n$ that satisfy all conditions, any of them will be accepted.