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 $ .