Problem Statement

You are given integers N and K.
Let us call an integer sequence $A=(A_1,A_2,\cdots,A_N)$ good when it satisfies all of the conditions below.

• $0 \leq A_i \leq i (1 \leq i \leq N)$
• For every integer $v=1,2,\cdots,N,$ there is at most one index i such that A_i=v.

Find the sum, modulo (10^9+7), of the answers to the following problem for all good sequences A.

• Find the number of length-K (not necessarily contiguous) subsequences of A consisting of positive integers that are decreasing. In other words, find the number of sequences of indices $1 \leq i_1 < i_2 < \cdots < i_K \leq N$ such that $A_{i_1}>A_{i_2}>\cdots>A_{i_K} \geq 1$.

Input

Input is given from Standard Input in the following format:
N K

Output

Print the answer.

Constraints

• $3 \leq N \leq 5000$
• $2 \leq K$
• $2K-1 \leq N$
• All values in input are integers.

Sample Input 1

3 2

Sample Output 1

1

For example, A=(0,2,1) is a good sequence, with one subsequence satisfying the condition.
There are other good sequences such as A=(0,1,0),(1,2,3),(0,0,0), but none of them has subsequences satisfying the condition.
In the end, no good sequence other than A=(0,2,1) has subsequences satisfying the condition, so the answer is 1.

Sample Input 2

6 2

Sample Output 2

660

Sample Input 3

10 3

Sample Output 3

242595

Sample Input 4

100 10

Sample Output 4

495811864

见题面 Input 部分

见题面 Output 部分