2012 AIME I Problem 11

A frog begins at P_0 = (0,0) and makes a sequence of jumps according to the following rule: from P_n = (x_n, y_n), the frog jumps to P_{n+1}, which may be any of the points (x_n + 7, y_n + 2), (x_n + 2, y_n + 7), (x_n - 5, y_n - 10), or (x_n - 10, y_n - 5). There are M points (x, y) with |x| + |y| \le 100 that can be reached by a sequence of such jumps. Find the remainder when M is divided by 1000.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.