You are at $$$(0, 0)$$$ in a rectangular grid and want to go to $$$(x, y)$$$.

In order to do so, you are allowed to perform a sequence of steps.

Each step consists of moving a positive integer amount of length in the positive direction of either the $$$x$$$ or the $$$y$$$ axis.

The first step must be along the $$$x$$$ axis, the second along the $$$y$$$ axis, the third along the $$$x$$$ axis, and so on. Formally, if we number steps from one in the order they are done, then odd-numbered steps must be along the $$$x$$$ axis and even-numbered steps must be along the $$$y$$$ axis.

Additionally, each step must have a length strictly greater than the length of the previous one.

Output the minimum number of steps needed to reach $$$(x, y)$$$, or $$$-1$$$ if it is impossible.

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 first and only line of each case contains two integers $$$x$$$ and $$$y$$$ ($$$1 \le x, y \le 10^9$$$).

Output

For each test case, output the minimum number of steps to reach $$$(x, y)$$$ or $$$-1$$$ if it is impossible.

Note

Visualizer link

In the second test case, you can move to $$$(5, 0)$$$ by moving $$$5$$$ along the $$$x$$$ axis and then to $$$(5, 6)$$$ by moving $$$6$$$ along the $$$y$$$ axis.

$\text{[math]}$ In the third test case, you can move to $$$(1, 0)$$$, then to $$$(1, 2)$$$, and finally to $$$(4, 2)$$$. $\text{[math]}$ In the fourth test case, reaching $$$(1, 1)$$$ is impossible since after moving to $$$(1, 0)$$$ along the $$$x$$$ axis, you are forced to move at least $$$2$$$ along the $$$y$$$ axis.

Shortest Increasing Path

Examples