Scooby-Doo is fond of adventures. This time he wanted to find a hiding-place in
a vampire castle. After a long search, Scooby ended up in a huge rectangular
hall with four entrances, one in each corner, through one of which he had
entered. The floor was paved with white square tiles. Scooby thought that the
hiding-place was under one of these tiles. He started searching for it by
turning the tiles over, the grey side up. He began his search from a corner
moving at an angle of 45° to the walls. Each time he came to a wall,
he made a 90° turn. If he stepped on a grey tile, he turned it back the white
side up. The search went on until Scooby reached an entrance at one of the
corners. Then, not having found the hiding-place, the tired dog sighed and went
out to have a snack.

Given the dimensions of the hall, calculate the total
number of tiles that were turned the grey side up at the end of the search.

### Input

The only input line contains integers *n* and *m* separated with a space.
They are the length and width of the hall measured in tiles
(2 ≤ *n*, *m* ≤ 1 000 000).

### Output

In the only line output the number of grey tiles in the hall after Scooby-Doo's
search.

### Samples

**Problem Author: **Alexander Larin

**Problem Source: **XI USU Open Personal Contest (March 13, 2010)