a) Find the largest possible value of the number $x_1x_2 + x_2x_3 + ... + x_{n-1}x_n$, if $x_1, x_2, ... , x_n$ ($n \ge 2$) are non-negative integers and their sum is $2011$. b) Find the numbers $x_1, x_2, ... , x_n$ for which the maximum value determined at a) is obtained