Combinatorics Confusion

${\sum^{650} _{x+y=650}}\large \dbinom{2x}{x} \dbinom{2y}{y}$

If $x$ and $y$ are non-negative integers, find S, if:
summation mod 7 = a;
summation mod 8 = b;
summation mod 9 = c;
summation mod 10 = d; and
S = a + b + c + d.