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 $10^9 + 7$.
### Constraints
- $1 \le n \le 2 \times 10^5$
- $1 \le k \le n$
### Example
Input:
```
4 2
```
Output:
```
8
```
There are $8$ ways, with letter `y` denoting yellow and letter `o` denoting orange:
- `oyyy`
- `yoyy`
- `yyoy`
- `oyoy`
- `oyyo`
- `yoyo`
- `yyyo`
- `yyyy`
