Problem Statement

There are $N+1$ squares arranged in a row, numbered $0,1,\dots,N$ from left to right. Each of the squares numbered $1$ through $N$ has $1$ piece placed on it.
Here, for an integer sequence $A$ of length $K$ with elements between $1$ and $N$ inclusive and $\large \textbf{all elements pairwise distinct}$, define its score as the sum of the numbers of the squares that have at least $1$ piece on them after performing the following operation.

Operation: for $i=1,2,\dots,K$ in this order, move all pieces on square $A_i$ to square $A_i-1$

There are ${}_N\mathrm {P}_ K$ integer sequences of length $K$ with elements between $1$ and $N$ inclusive and $\large \textbf{all elements pairwise distinct}$.
Compute the score for every integer sequence with $\large \textbf{all elements pairwise distinct}$, and find the sum of the scores modulo $10^9+7$.

Input

$N$ $K$

$1\le K\le N\le 10^5$

Output

Output the sum of the scores over all integer sequences with $\large \textbf{all elements pairwise distinct}$, modulo $10^9+7$. Print a newline at the end.

Sample

6 4

3600

1 1

0

1000 100

45281982