It is known that, for all positive integers $$k$$, $$1^2+2^2+3^2+\ldots+k^{2}=\frac{k(k+1)(2k+1)}6$$. Find the smallest positive integer $$k$$ such that $$1^2+2^2+3^2+\ldots+k^2$$ is a multiple of $$200$$.

(第二十届AIME2 2002 第7题)