Binomial Theorem

Let K be the sum of the coefficients of the odd powers of $x$ in the expansion of $(1+x)^{99}$. Let $a$ be the middle term in the expansion of ${\left( {2 + {1 \over {\sqrt 2 }}} \right)^{200}}$. If ${{{}^{200}{C_{99}}K} \over a} = {{{2^l}m} \over n}$, where m and n are odd numbers, then the ordered pair $(l,\mathrm{n})$ is equal to