Time Limit : sec, Memory Limit : KB

Balls and Boxes 4

BallsBoxesAny wayAt most one ballAt least one ball
DistinguishableDistinguishable123
IndistinguishableDistinguishable456
DistinguishableIndistinguishable789
IndistinguishableIndistinguishable101112

Problem

You have $n$ balls and $k$ boxes. You want to put these balls into the boxes.

Find the number of ways to put the balls under the following conditions:

• Each ball is not distinguished from the other.
• Each box is distinguished from the other.
• Each ball can go into only one box and no one remains outside of the boxes.
• Each box can contain an arbitrary number of balls (including zero).

Note that you must print this count modulo $10^9+7$.

Input

$n$ $k$


The first line will contain two integers $n$ and $k$.

Output

Print the number of ways modulo $10^9+7$ in a line.

Constraints

• $1 \le n \le 1000$
• $1 \le k \le 1000$

Sample Input 1

5 3


Sample Output 1

21


Sample Input 2

10 5


Sample Output 2

1001


Sample Input 3

100 100


Sample Output 3

703668401