A set is called a good set if every element is a positive integer not exceeding $N$, and any two distinct elements of the set have an absolute difference of at least $M$.

Find the number of good sets modulo ${10}^9+7$.

Constraints

$1\le M\le N\le {10}^6$

Subtask 1 [10%]

$1\le N\le 10$

Subtask 2 [30%]

$1\le N\le {10}^4$

Subtask 3 [60%]

No additional constraints.

Input Specification

The only line contains two space-separated integers, $N$ and $M$.

Output Specification

Output the number of good sets modulo ${10}^9+7$.

Sample Input

4 3

Sample Output

6

Explanation for Sample

The good sets are $\{\},\{1\},\{2\},\{3\},\{4\},\{1,4\}$.