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 $(n, m)$ ?

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.

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.

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 $6$ .