Super Poker 

I have a set of super poker cards, consisting of an infinite number of cards. For each positive integer p, there are exactly four cards whose value is p: Spade(S), Heart(H), Club(C) and Diamond(D). There are no cards of other values.

Given two positive integers n and k, how many ways can you pick up at most k cards whose values sum to n? For example, if n = 15 and k = 3, one way is 3H + 4S + 8H, shown below:

Input 

There will be at most 20 test cases, each with two integers n and k ( 1$\le$n$\le$10⁹, 1$\le$k$\le$10). The input is terminated by n = k = 0.

Output 

For each test case, print the number of ways, modulo 1,000,000,009.

Sample Input 

2 1
2 2
2 3
50 5
0 0

Sample Output 

4
10
10
1823966

The Seventh Hunan Collegiate Programming Contest
Problemsetter: Rujia Liu, Special Thanks: Jane Alam Jan