Let \( S_{K}=\frac{1+2+\ldots .+K}{K} \) and \( \sum_{j=1}^{n} S_{j}^{2}=\frac{n}{A}\left(B n^{2}+C n+D\right) \), where…

Let \( S_{K}=\frac{1+2+\ldots .+K}{K} \) and

\( \sum_{j=1}^{n} S_{j}^{2}=\frac{n}{A}\left(B n^{2}+C n+D\right) \), where \( A, B, C, D \in N \)

and \( A \) has least value. Then

[JEE Main 2023, 08 Apr (Shift 1)]