JEE Math Practice Question

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

1. A.(50, 101)
2. B.(50, 51)
3. C.(51, 101)
4. D.(51, 99)