2002 AIME II Problem 7

It is known that, for all positive integers \mathrm{k},

$$1^{2}+2^{2}+3^{2}+\cdots+k^{2}=\frac{k(k+1)(2 k+1)}{6}$$

Find the smallest positive integer k such that 1^{2}+2^{2}+3^{2}+\cdots+k^{2} is a multiple of 200 .