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:

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

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