William has two numbers $a$ and $b$ initially both equal to zero. William mastered performing three different operations with them quickly. Before performing each operation some positive integer $k$ is picked, which is then used to perform one of the following operations: (note, that for each operation you can choose a new positive integer $k$)

1. add number $k$ to both $a$ and $b$, or
2. add number $k$ to $a$ and subtract $k$ from $b$, or
3. add number $k$ to $b$ and subtract $k$ from $a$.

Note that after performing operations, numbers $a$ and $b$ may become negative as well.

William wants to find out the minimal number of operations he would have to perform to make $a$ equal to his favorite number $c$ and $b$ equal to his second favorite number $d$.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). Description of the test cases follows.

The only line of each test case contains two integers $c$ and $d$ $(0 \le c, d \le 10^9)$, which are William's favorite numbers and which he wants $a$ and $b$ to be transformed into.

For each test case output a single number, which is the minimal number of operations which William would have to perform to make $a$ equal to $c$ and $b$ equal to $d$, or $-1$ if it is impossible to achieve this using the described operations.