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}=\left(x_{n}, y_{n}\right), the frog jumps to P_{n+1}, which may be any of the points \left(x_{n}+7, y_{n}+2\right),\left(x_{n}+2, y_{n}+7\right),\left(x_{n}-5, y_{n}-10\right), or \left(x_{n}-10, y_{n}-5\right). There are M points (x, y) with |x|+|y| \leq 100 that can be reached by a sequence of such jumps. Find the remainder when M is divided by 1000 .