Little Elephant and Mouses

It is well-known that the elephants are afraid of mouses. The Little Elephant from the Zoo of Lviv is not an exception. The Little Elephant is on a board A of n rows and m columns (0-based numeration). At the beginning he is in cell with coordinates (0; 0) and he wants to go to cell with coordinates (n-1; m-1). From cell (x; y) Little Elephant can go either to (x+1; y) or (x; y+1). Each cell of