Padaengi's Cake Stacking

Padaengi has loved sweet food since childhood, and wanted to make sweets with her own hands, so she took an internship at a food company.

The first task Padaengi receives is stacking $N$ cake layers. Padaengi must finish $K$ cakes every day. Each cake is stacked from the bottom layer to the top layer in order. Layer 1 can be placed right away. For an integer $i \ge 1$, layer $i+1$ can be placed only on a cake whose stack has layers 1 through $i$ and nothing above.

While working every day, Padaengi noticed that she often receives a layer that cannot be placed. She considers this a serious problem for her work efficiency. To raise the issue, she decided to report the probability that no layer that cannot be placed is received during the work, when the layers are given in a random order. Calculate this probability for Padaengi!

The first line contains the number of cake layers $N$ and the number of cakes $K$ to make, separated by a space. ($1 \le N \le 1{,}000$, $1 \le K \le 1{,}000$)

When $N \times K$ cake layers are given in a random order, let the probability that no layer that cannot be placed is received during the work be $p / q$. Print $p \times q^{-1} \pmod{1{,}000{,}000{,}007}$. Here $q^{-1}$ is the modular multiplicative inverse of $q$, and $p$ and $q$ are coprime. Under the given constraints, the value of $p \times q^{-1} \pmod{1{,}000{,}000{,}007}$ is proven to exist uniquely.

$1{,}000{,}000{,}007 = 10^9+7$

The $N \times K$ cake layers consist of $K$ layers each of $N$ types.