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\}~.