Binary Shuffle

Chef has two integers $A$ and $B$. He can perform the following operation on $A$ an arbitrary number of times (including zero): - write $A$ as a binary number with an arbitrary number of leading zeroes (possibly without any) - shuffle the binary digits of $A$ in an arbitrary way, obtaining a number $s$ - replace $A$ by $s+1$ Chef is wondering about the minimum number of operations he has to perfo