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.

In the third test case, you can move to $(1, 0)$, then to $(1, 2)$, and finally to $(4, 2)$.

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.