CF2147A.Shortest Increasing Path

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.

你位于矩形网格中的点 $(0, 0)$，目标是到达点 $(x, y)$。

为此，你可以执行一系列移动步骤。

每一步必须沿 $x$ 轴或 $y$ 轴的正方向移动一个正整数长度。

第一步必须沿 $x$ 轴，第二步沿 $y$ 轴，第三步沿 $x$ 轴，依此类推。形式化地说，若将步骤按执行顺序从 $1$ 开始编号，则奇数编号的步骤必须沿 $x$ 轴，偶数编号的步骤必须沿 $y$ 轴。

此外，每一步的长度必须严格大于前一步的长度。

输出到达 $(x, y)$ 所需的最少步数；若无法到达，则输出 $-1$。

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 $y$ ($1 \le x, y \le 10^9$).

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^4$）。随后是各测试用例的描述。

每个测试用例仅有一行，包含两个整数 $x$ 和 $y$（$1 \le x, y \le 10^9$）。

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

对于每个测试用例，输出到达 $(x, y)$ 所需的最少步数；如果无法到达，则输出 $-1$。

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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.

可视化链接

在第二个测试用例中，你可以先沿 $x$ 轴移动 $5$ 个单位到达 $(5, 0)$，再沿 $y$ 轴移动 $6$ 个单位到达 $(5, 6)$。

在第三个测试用例中，你可以先移动到 $(1, 0)$，再移动到 $(1, 2)$，最后移动到 $(4, 2)$。

在第四个测试用例中，无法到达 $(1, 1)$，因为沿 $x$ 轴移动到 $(1, 0)$ 后，你必须至少沿 $y$ 轴移动 $2$ 个单位。