Game of Stones
A playing board consists of 50 squares arranged side-by-side from left to right. You start with a stone on the leftmost square. During each turn of the game you are allowed to move the stone to the right by 1, 2, 3, 4 or 5 squares.
Let M be the number of different ways in which you can reach the rightmost square in at most 15 moves. Find the last three digits of M.