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