Simplified quantum algorithm for the oracle identification problem

In the oracle identification problem we have access to bits of an unknown string x length n, with promise that it belongs a known set $$C\subseteq \{0,1\}^{n}$$ . The goal is identify using as few queries possible. We develop quantum query algorithm for this complexity $$O\left (\sqrt {\frac {n\log M }{\log (n/\log M)+1}}\right )$$ , where size C. This bound already derived by Kothari in 2014, which provide more elegant simpler proof.