You are given two positive integers $x$ and $y$ ($1\le x, y\le 10^9$).

Find a non-negative integer $k\le 10^{18}$, such that $(x+k) + (y+k) = (x+k)\oplus (y+k)$ holds$^{\text{∗}}$, or determine that such an integer does not exist.

$^{\text{∗}}$$\oplus$ denotes the bitwise XOR operation.

Input

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 two integers $x$ and $y$ ($1\le x, y\le 10^9$) — the given integers.

Output

For each test case, output a single integer $k$ ($0\le k\le 10^{18}$) — the integer you found. Print $-1$ if it is impossible to find such an integer.

If there are multiple answers, you may print any of them.

Note

In the first test case, since $(2 + 0) + (5 + 0) = (2 + 0) \oplus (5 + 0) = 7$, $k=0$ is a possible answer. Note that $k=4$ is also a possible answer because $(2 + 4) + (5 + 4) = (2 + 4) \oplus (5 + 4) = 15$.

In the second test case, $(x+k)\oplus (y+k) = (6+k)\oplus (6+k) = 0$. However, $(x+k)+(y+k) \gt 0$ holds for every $k \ge 0$, implying that such an integer $k$ does not exist.