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.*;

class Main{

    void solve(){
        Scanner sc = new Scanner(System.in);

        int max = 1130;
        boolean[] prime = new boolean[max];
        for(int i=2; i<max; i++) prime[i] = true;
        for(int i=2; i<prime.length; i++){
            for(int j=i*2; j<prime.length; j+=i){
                prime[j] = false;
            }
        }

        int[][] dp = new int[15][max];
        /*
        for(int i=0; i<max; i++){
            if(prime[i]) dp[1][i] = 1;
        }
        */
        dp[0][0] = 1;
        for(int i=0; i<max; i++){
            if(!prime[i]) continue;
            for(int j=14; j>=1; j--){
                for(int k=max-1; k>=i; k--){
                    dp[j][k] += dp[j-1][k-i];
                }
            }
        }

        int n = sc.nextInt();
        int k = sc.nextInt();
        while(n!=0 || k!=0){
            System.out.println(dp[k][n]);
            n = sc.nextInt();
            k = sc.nextInt();
        }
    }

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