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## J. Search for a Hiding-Place

Time limit: 0.5 second
Memory limit: 64 MB
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

inputoutput
7 5
11
2 3
3
Problem Author: Alexander Larin
Problem Source: XI USU Open Personal Contest (March 13, 2010)
To submit the solution for this problem go to the Problem set: 1762. Search for a Hiding-Place