p00848 Sum of Different Primes_13765
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{
    static int[] p = new int[1130];
    static int pnum;
    static int[][][] dp;

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

	calcPrimes();

	int n = sc.nextInt();
	int k = sc.nextInt();

	while(n!=0){

	    dp = new int[1121][15][188];
	    for(int i=0; i<=n; i++)
		for(int j=0; j<=k; j++)
		    for(int l=0; l<188; l++)dp[i][j][l] = -1;
	    System.out.println(solve(n,k,0));

	    n = sc.nextInt();
	    k = sc.nextInt();
	}
    }

    public static int solve(int n, int k, int idx){
	if(n==0 && k==0){return 1;}
	else if(n==0 || k==0){return 0;}
	if(dp[n][k][idx]>=0){return dp[n][k][idx];}
	
	int res = 0;
	for(int i=idx; i<pnum; i++){
	    if(p[i]>n){
		break;
	    }else{
		res += solve(n-p[i],k-1,i+1);
	    }
	}

	return dp[n][k][idx] = res;
    }

    public static void calcPrimes(){
	p[0] = 2;
	pnum = 1;
	for(int i=3; i<=1120; i+=2){
	    boolean add = true;
	    for(int j=0; j<pnum; j++){
		if(p[j]*p[j]>i){break;}
		if(i%p[j]==0){
		    add = false;
		    break;
		}
	    }
	    if(add){p[pnum++] = i;}
	}
    }
}