Problem Statement

There is a circle on a plane. It has $N$ distinct points on its circumference, numbered $1,2,\dots,N$ in clockwise order.

There are $\frac{N(N-1)}{2}$ line segments that can be drawn by connecting two different points among the $N$ points; you will choose and draw $M$ of these segments. Find the number, modulo $(10^9+7)$, of ways to draw $M$ segments such that no two of them intersect at a point other than their endpoints.

Constraints

• $1 \le N \le 10^7$
• $0 \le M \le \frac{N(N-1)}{2}$

Input

The input is given from Standard Input in the following format:

N M

Output

Print the answer.