Time Limit : sec, Memory Limit : KB
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Balls and Boxes 12

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 not distinguished from the other.
  • Each ball can go into only one box and no one remains outside of the boxes.
  • Each box must contain at least one ball.

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

10 5

Sample Output 1

7

Sample Input 2

30 15

Sample Output 2

176

Sample Input 3

100 30

Sample Output 3

3910071