# Grover algorithm for known number of solutions

I am reading Computational Complexity book and specifically Grovers search algorithm. I am aware that if we knew in advance exact number of solutions $K$, then the basic algorithm can be tweaked to find an input $x$ in $O(\sqrt{2^{|x|}/K})$ time. I found some material but, as I am new to quantum computing, I have problem connecting it to the explanation given in this book. Can anybody present the basic idea?