Permutations and Increasing Sequences

Geondeok, who liked playing with permutations, found a beautiful property in a sequence he built. His permutation $A$ satisfies two conditions. First, $A$ contains every integer from 1 to $N$ exactly once. Second, the sequence $B$ formed by adding $K$ consecutive terms of $A$ is an increasing sequence. That is, $B_i = A_i + A_{i+1} + \cdots + A_{i+K-1}$ for $1 \le i \le N-K+1$.

For example, if $A = \{1, 3, 2, 5, 4\}$ and $K = 3$, then $B = \{6, 10, 11\}$, so both conditions hold.

Geondeok wants to know how many permutations $A$ have this property. Help him count, for given $N$ and $K$, the permutations of length $N$ that satisfy both conditions.

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

Print the number of permutations of length $N$ that satisfy the property, modulo $10^9+7$.