A14385. A Variety of Operations

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.

Let us demonstrate one of the suboptimal ways of getting a pair $(3, 5)$ :

- Using an operation of the first type with $k=1$ , the current pair would be equal to $(1, 1)$ .
- Using an operation of the third type with $k=8$ , the current pair would be equal to $(-7, 9)$ .
- Using an operation of the second type with $k=7$ , the current pair would be equal to $(0, 2)$ .
- Using an operation of the first type with $k=3$ , the current pair would be equal to $(3, 5)$ .