CONO-SUR 2016 Problem 2

For every $k= 1,2, \ldots$ let $s_k$ be the number of pairs $(x,y)$ satisfying the equation $kx + (k+1)y = 1001 - k$ with $x$ , $y$ non-negative integers. Find $s_1 + s_2 + \cdots + s_{200}$ .