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.Arrays;
import java.util.Scanner;

//Sum of Different Primes
public class Main{

	int N = 1120, num;
	int[] p;
	int[][][] dp;
	
	int get(int x, int index, int rest){
		if(rest==0){
			if(x==0)return dp[x][index][rest] = 1;
			else return dp[x][index][rest] = 0;
		}
		if(dp[x][index][rest]!=-1)return dp[x][index][rest];
		int res = 0;
		for(int i=index;i<num;i++){
			if(x<p[i])break;
			res += get(x-p[i], i+1, rest-1);
		}
		return dp[x][index][rest] = res;
	}
	
	void run(){
		num = 0;
		p = new int[187];
		boolean[] prime = new boolean[N+1];
		Arrays.fill(prime, true);
		prime[0]=prime[1]=false;
		for(int i=2;i<=N;i++)if(prime[i]){
			p[num++] = i;
			for(int j=i+i;j<=N;j+=i)prime[j]=false;
		}
		dp = new int[N+1][num+1][15];
		for(int i=0;i<=N;i++)for(int j=0;j<=num;j++)for(int k=0;k<=14;k++)dp[i][j][k]=-1;
		Scanner sc = new Scanner(System.in);
		for(;;){
			int n = sc.nextInt(), k = sc.nextInt();
			if((n|k)==0)break;
			System.out.println(get(n, 0, k));
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}
}