Beautiful Permutation

Consider a permutation $P$ of length $N$. We call a subarray of $P$ good if it contains the value $X$. Consider a set $S$ containing maximum elements of all good subarrays of $P$. Permutation $P$ is called **beautiful** if $S$ contains exactly $K$ **distinct** values. Given three integers $N$, $X$, and $K$, you need to find the number of beautiful permutations of length $N$. Since this number c