A positive integer may be expressed as a sum of different prime numbers (primes), in one way or another. Given two positive integers n and k, you should count the number of ways to express n as a sum of k different primes. Here, two ways are considered to be the same if they sum up the same set of the primes. For example, 8 can be expressed as 3 + 5 and 5+ 3 but they are not distinguished.

When n and k are 24 and 3 respectively, the answer is two because there are two sets {2, 3, 19} and {2, 5, 17} whose sums are equal to 24. There are no other sets of three primes that sum up to 24. For n = 24 and k = 2, the answer is three, because there are three sets {5, 19}, {7,17} and {11, 13}. For n = 2 and k = 1, the answer is one, because there is only one set {2} whose sum is 2. For n = 1 and k = 1, the answer is zero. As 1 is not a prime, you shouldn't count {1}. For n = 4 and k = 2, the answer is zero, because there are no sets of two diffrent primes whose sums are 4.

Your job is to write a program that reports the number of such ways for the given n and k.



Input

The input is a sequence of datasets followed by a line containing two zeros separated by a space. A dataset is a line containing two positive integers n and k separated by a space. You may assume that n ≤ 1120 and k ≤ 14.

Output

The output should be composed of lines, each corresponding to an input dataset. An output line should contain one non-negative integer indicating the number of ways for n and k specified in the corresponding dataset. You may assume that it is less than 231.

Example

Input

24 3
24 2
2 1
1 1
4 2
18 3
17 1
17 3
17 4
100 5
1000 10
1120 14
0 0


Output

2
3
1
0
0
2
1
0
1
55
200102899
2079324314
import java.util.*;

public class Main{
	public static int[][][] dp;

	public static boolean[] primes(int n){
		boolean[] primes = new boolean[n+1];
		Arrays.fill(primes, true);
		primes[0] = primes[1] = false;
		for(int i=2;i<=n;i++){
			if(primes[i]){
				for(int j=i*2;j<=n;j+=i){
					primes[j] = false;
				}
			}
		}
		return primes;
	}

	public static int dfs(int i,int n,int k,ArrayList<Integer> p){
		if(n == 0){
			if(k == 0) return 1;
			else return 0;
		}
		else if(k == 0) return 0;
		if(dp[i][n][k] != -1) return dp[i][n][k];

		int res = 0;
		for(int j=i;p.get(j)<=n;j++){
			res += dfs(j+1,n-p.get(j),k-1,p);
		}
		return dp[i][n][k] = res;
	}

	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);

		boolean[] flg = primes(1200);
		ArrayList<Integer> p = new ArrayList<Integer>();
		for(int i=0;i<flg.length;i++) if(flg[i]) p.add(i);

		int size = p.size();
		dp = new int[size][1121][15];
		for(int i=0;i<size;i++) for(int j=0;j<1121;j++) for(int k=0;k<15;k++) dp[i][j][k] = -1;

		while(true){
			int n=sc.nextInt(), k=sc.nextInt();
			if(n==0 && k==0) break;
			System.out.println(dfs(0,n,k,p));
		}
	}
}