$\text{[math]}$

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 $$$k$$$)

add number $$$k$$$ to both $$$a$$$ and $$$b$$$, or
add number $$$k$$$ to $$$a$$$ and subtract $$$k$$$ from $$$b$$$, or
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 $$$d$$$.

Input

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.

Output

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.

Note

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 $$$(3, 5)$$$.

A Variety of Operations

Examples