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

  1. 00100
  1. 00101
  1. 00110
  1. 00111
  1. 01001
  1. 01010
  1. 01011
  1. 01100
  1. 01101
  1. 01110
  1. 01111
  1. 10010
  1. 10011
  1. 10100
  1. 10101
  1. 10110
  1. 10111
  1. 11001
  1. 11010
  1. 11011
  1. 11100
  1. 11101
  1. 11110
  1. 11111
Β 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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