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 static java.lang.Math.*;
import static java.util.Arrays.*;

import java.util.*;
import java.io.*;

public class Main {
	int n, k, m;
	ArrayList<Integer> ps;
	int N = 1120;
	int mem[][][];
	
	void run() {
		Scanner sc = new Scanner(System.in);
		prime();
		for(;;) {
			n = sc.nextInt(); k = sc.nextInt();
			if((n|k) == 0) break;
			mem = new int[n+1][k+1][m+1];
			for(int[][] a: mem) for(int[] b: a) fill(b, -1);
			System.out.println(solve(0, 0, 0));
		}
	}
	
	int solve(int sum, int num, int i) {
		if( i == m+1 || sum > n || num > k ) return 0;
		if( mem[sum][num][i] >= 0 ) return mem[sum][num][i];
		if( k == num ) {
			if( sum == n ) return mem[sum][num][i] = 1;
		}
		
//		debug(sum, num, i);
		int cnt = 0;
		for(int j=i;j<m && sum+ps.get(j)<=n;j++) cnt += solve(sum+ps.get(j), num+1, j+1);
		return mem[sum][num][i] = cnt;
	}
	
	void prime() {
		boolean[] p = new boolean[N+1];
		ps = new ArrayList<Integer>();
		for(int i=2;i<=N;i++) if(!p[i]) {
			for(int j=2*i;j<=N;j+=i) p[j] = true;
			ps.add(i);
		}
		m = ps.size(); 
	}

	void debug(Object... os) {
		System.err.println(Arrays.deepToString(os));
	}

	public static void main(String[] args) {
		new Main().run();
	}
}