Marisa's wooden fence is made up of n planks. Marisa wants to repaint the fence using two colors: orange and yellow. The dominant color of the fence will be yellow with a little bit of orange. Therefore, Marisa wants any two orange planks to be at least k planks apart. The distance between two planks at positions i and j is |i−j|. How many ways are there to paint the fence such that this condition is satisfied?
### Input
- A single line containing two integers n and k.
### Output
- Output a single integer representing the number of ways to paint the fence, modulo 109+7.
### Constraints
- 1≤n≤2×105
- 1≤k≤n
### Example
Input:
42
Output:
8
There are 8 ways, with letter y denoting yellow and letter o denoting orange:
- oyyy
- yoyy
- yyoy
- oyoy
- oyyo
- yoyo
- yyyo
- yyyy
