Mex Array

Given an array $A$ containing $N$ non-negative integers, you have to create a new array $B$ that is formed in the following way: While $A$ is not empty: 1. Choose an integer $k$ ($1 \leq k \leq |A|$). Here, $|A|$ denotes the current length of $A$. 2. Choose $k$ elements of $A$. 3. Append the MEX of these chosen elements to the end of array $B$, and erase them from the array $A$. That is, in e