Range MEX

You are given an array $A$ of $N$ non-negative integers. In one move, you can do the following: - choose $(L, R)$ such that $1 \le L \le R \le |A|$. - Let $X = \text{MEX}^{\dagger}([A_L, A_{L + 1}, \ldots, A_R])$. - Insert $X$ into the array $A$ in any position (possibly at the start or end). Given an integer $K$, find the minimum moves needed to insert $K$ into the array. Note that you need to