Counting Is Fun

For a permutation $X$ of length $M$, let $F(X,K)$ denote the number of arrays $A$ of size $K$ such that: - $1 \leq A_i \leq M$ ; - $A_{i-1} \leq A_{i}$ for all $2 \leq i \leq K$ ; - $\min\limits_{j = 1}^{A_1} X_j = \min\limits_{j = 1}^{A_i} X_j$ for all $ 1 \leq i \leq K$ You are given three positive integers $N, K,$ and $V$. Find the sum of $F(P,K)$ over all $(N-1)!$ permutations of $P = [