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)]