CF1668A.Direction Change

You are given a grid with $n$ rows and $m$ columns. Rows and columns are numbered from $1$ to $n$, and from $1$ to $m$. The intersection of the $a$-th row and $b$-th column is denoted by $(a, b)$.

Initially, you are standing in the top left corner $(1, 1)$. Your goal is to reach the bottom right corner $(n, m)$.

You can move in four directions from $(a, b)$: up to $(a-1, b)$, down to $(a+1, b)$, left to $(a, b-1)$ or right to $(a, b+1)$.

You cannot move in the same direction in two consecutive moves, and you cannot leave the grid. What is the minimum number of moves to reach $(n, m)$?

你被给定一个 $n$ 行 $m$ 列的网格。行和列均从 $1$ 编号至 $n$ 和从 $1$ 编号至 $m$。第 $a$ 行与第 $b$ 列的交点记为 $(a, b)$。

初始时，你位于左上角 $(1, 1)$。你的目标是到达右下角 $(n, m)$。

你可以从 $(a, b)$ 向四个方向移动：向上至 $(a-1, b)$、向下至 $(a+1, b)$、向左至 $(a, b-1)$ 或向右至 $(a, b+1)$。

你不能在连续两步中沿相同方向移动，且不能移出网格边界。问：到达 $(n, m)$ 所需的最少移动步数是多少？

The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^3$) — the number of the test cases. The description of the test cases follows.

The first line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 10^9$) — the size of the grid.

输入包含多个测试用例。第一行包含一个整数 $t$（$1 \le t \le 10^3$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $m$（$1 \le n, m \le 10^9$），表示网格的大小。

For each test case, print a single integer: $-1$ if it is impossible to reach $(n, m)$ under the given conditions, otherwise the minimum number of moves.

对于每个测试用例，输出一个整数：若在给定条件下无法到达 $(n, m)$，则输出 $-1$；否则输出最少移动步数。

Test case $1$: $n=1$, $m=1$, and initially you are standing in $(1, 1)$ so $0$ move is required to reach $(n, m) = (1, 1)$.

Test case $2$: you should go down to reach $(2, 1)$.

Test case $3$: it is impossible to reach $(1, 3)$ without moving right two consecutive times, or without leaving the grid.

Test case $4$: an optimal moving sequence could be: $(1, 1) \to (1, 2) \to (2, 2) \to (2, 1) \to (3, 1) \to (3, 2) \to (4, 2)$. It can be proved that this is the optimal solution. So the answer is $6$.

测试用例 $1$：$n=1$，$m=1$，初始时你位于 $(1, 1)$，因此到达 $(n, m) = (1, 1)$ 所需移动次数为 $0$。

测试用例 $2$：你需要向下移动以到达 $(2, 1)$。

测试用例 $3$：若不连续向右移动两次，或不移出网格边界，则无法到达 $(1, 3)$。

测试用例 $4$：一种最优移动序列为：$(1, 1) \to (1, 2) \to (2, 2) \to (2, 1) \to (3, 1) \to (3, 2) \to (4, 2)$。可以证明该序列是最优解。因此答案为 $6$。