A fixed point for a function $f$ is a value $x$ such that $f(x)=x$.

In this task we focus on the following function: $$f(x) = ((a \cdot x) \oplus b) \bmod 2^{64}$$The operator $\oplus$ is the xor operator (written ^ in C++/Java).

Given $a$ and $b$, can you find a fixed point for the function?

Input

The first input line contains an integer $t$: the number of test cases.

After this, there are $t$ lines that describe the test cases. Each line contains two integers $a$ and $b$.

All test cases have been generated so that $a$ and $b$ have been chosen uniformly randomly from the range $0 \ldots 2^{64}-1$.

Output

For each case, output a number $0\leq x\leq 2^{64}-1$ that is a fixed point for the function, or "-" if no such number exists.

If there are several possible solutions, you can output any of them.

Constraints

• $1 \le t \le 10^5$
• $0\leq a, b\leq 2^{64}-1$

Example

Input:

3
2 5
1 1
0 7

Output:

3
-
7

For example, in the first test case, $f(3)=((2\cdot3) \oplus 5) \bmod 2^{64}=3$.