A. Robot Odd Moves
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a point $$$(a, b)$$$ of the integer grid.

A robot is standing at the point $$$(0, 0)$$$. The robot may perform the following two-step operation any number of times (possibly zero), where $$$(x, y)$$$ denotes the point the robot is standing at:

  1. Move one unit up or one unit down: $$$(x, y) \rightarrow (x, y + 1)$$$ or $$$(x, y) \rightarrow (x, y - 1)$$$.
  2. Then move one unit to the right: $$$(x, y) \rightarrow (x + 1, y)$$$.

The robot visits a point if at some moment it is standing at this point: before the first operation, between the two moves of an operation, or after an operation.

Find the minimum number of operations after which the robot has visited $$$(a, b)$$$, or determine that it is impossible.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). The description of the test cases follows.

The only line of each test case contains two integers $$$a$$$ and $$$b$$$ ($$$0 \le a, b \le 1000$$$) — the coordinates of the given point.

Output

For each test case, output a single integer — the minimum number of operations after which the robot has visited $$$(a, b)$$$, or $$$-1$$$ if it is impossible.

Example
Input
9
0 0
0 1
0 2
1 0
2 1
2 3
5 6
1000 999
1000 1000
Output
0
1
-1
2
3
3
6
1001
1000
Note

In the first example, the robot is standing at $$$(0, 0)$$$ before the first operation, so it has already visited $$$(0, 0)$$$ after $$$0$$$ operations.

In the second example, the robot moves up to $$$(0, 1)$$$ and then right to $$$(1, 1)$$$ during its first operation. Thus, it visits $$$(0, 1)$$$ after $$$1$$$ operation.

In the third example, it can be proven that the robot cannot visit $$$(0, 2)$$$.

In the fourth example, the robot can first move up and right, and then down and right. During the second operation, it visits $$$(1, 0)$$$. It cannot visit this point during the first operation, so the answer is $$$2$$$.