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;

public class Main {
    final double EPS = 1.0e-10;
    final int INF = 1 << 28;

    void run() {
        Scanner sc = new Scanner(System.in);
        int MAX = 1120;
        boolean[] isPrime = new boolean[MAX];
        int[] primes = new int[187];
        Arrays.fill(isPrime, true);
        int idx = 0;
        for (int i = 2; i < MAX; i++) {
            if (isPrime[i]) {
                primes[idx++] = i;
                for (int j = i * 2; j < MAX; j += i)
                    isPrime[j] = false;
            }
        }
        int dp[][][] = new int[187][MAX + 1][15];
        for (int i = 0; i < 187; i++) {
            for (int j = 0; j < MAX + 1; j++) {
                Arrays.fill(dp[i][j], 0);
                if (j == primes[i])
                    dp[i][j][1] = 1;
            }
        }
        for (int i = 0; i < 186; i++) {
            for (int j = 0; j < MAX + 1; j++) {
                for (int k = 1; k <= 14; k++) {
                    dp[i + 1][j][k] += dp[i][j][k];
                    if (j - primes[i+1] >= 0) {
                        dp[i + 1][j][k] += dp[i][j - primes[i+1]][k - 1];
                    }
                }
            }
        }
        while (true) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            if ((n | k) == 0)
                break;
            System.out.println(dp[186][n][k]);
        }

    }

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