codeforces#P1668A. Direction Change
Direction Change
Description
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.
Input
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.
Output
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.
Samples
6
1 1
2 1
1 3
4 2
4 6
10 5
0
1
-1
6
10
17
Note
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 $6$.