Beautiful bit-strings
We love bit-strings. We especially consider those beautiful if they don’t have
k consecutive 0s. Given a length n, can you count the number of different bit-strings of length n that are beautiful?Input
The input contains two integers
n and k (1 ≤ k ≤ n ≤ 1000).Output
The program should print the number of beautiful bit-strings of length n. As the answer can be very large, you are asked to print it modulo .
Examples
Input | Output |
5 2 | 24 |
Explanation
- 00100
- 00101
- 00110
- 00111
- 01001
- 01010
- 01011
- 01100
- 01101
- 01110
- 01111
- 10010
- 10011
- 10100
- 10101
- 10110
- 10111
- 11001
- 11010
- 11011
- 11100
- 11101
- 11110
- 11111
Constraints
Time limit: 2 seconds
Memory limit: 512 MB
Output limit: 1 MB