Asya & Number of Paths

Asya is a very intelligent girl and today she has come with a very interesting challenge for you. She has given you a matrix of size N x M. You have to travel through the matrix from (1, 1) to (N, M) and the only moves allowed from a cell (x, y) are (x + 1, y) or (x, y + 1). Sounds easy right !! Well, to make it lil more challenging, Asya has kept D disks on some cells of the matrix. She