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 …

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\({\left(2+\frac{1}{\sqrt{2}}\right)}^{200}\). If \(\frac{{}^{200}C_{99}K}{a}=\frac{{2}^{l}m}{n}\), where m and n are odd numbers, then the ordered pair (l, n) is equal to:

[JEE Main 2023, 29 Jan (Shift 2)]