Master of Permutation Construction

Master of Array Construction Jiro wants to count the permutations $P$ of length $N$ that satisfy the conditions below, given a sequence $A$ of length $N$. A permutation $P$ of length $N$ is a sequence that uses each integer from $1$ to $N$ exactly once.

• Sequence $B$ is defined as $(A_{P_1}, A_{P_2}, \ldots, A_{P_N})$.
• The annoyance of $B$ is the number of integers $i$ with $1 \le i \le N$ that satisfy the following condition.
  • $i=1$ or $\max(B_1, \ldots, B_{i-1}) < B_i$
• The annoyance of $B$ is at most $K$.

Find the number of permutations $P$ that satisfy the conditions, modulo $1\,000\,000\,007$.

The first line contains $N$ and $K$, separated by a space. ($1 \le N \le 5\,000$, $1 \le K \le N$)

The second line contains the sequence $A_1, A_2, \ldots, A_N$, separated by spaces. ($1 \le A_i \le 10^9$)

Print the number of permutations $P$ that satisfy the conditions, modulo $1\,000\,000\,007$.