402514: GYM100796 H Game of Corners

Alice is playing the Game of Corners. She is given a rectangular grid with n rows and m columns. During one move, Alice can choose any two previously unused cell borders that have a common point and join them in a corner (pictured). A corner can be oriented in any way.

Initially the grid is clear of corners. How many moves can Alice possibly make?

The only line of the input contains two integers n and m (1 ≤ n, m ≤ 10⁹) — the number of rows and the number of columns in the grid.

Output a single integer — the maximum number of moves Alice can make.

2 3

8

1 1

2

Two corners can share a point on the grid, but cannot share a cell border.

For the first given sample, one possible arrangement of corners is: