Sorting Segments

You are given a permutation $P$ of integers from $1$ to $N$, and an integer $K$ such that $\lceil \frac{2N}{3}\rceil \le K \le N$. In one operation, you can do the following: - Choose any consecutive segment of at most $K$ elements of the permutation, and sort it in increasing order. What's the smallest number of operations you have to make to sort the entire permutation in increasing order? ##