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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	Scanner sc = new Scanner(System.in);

	void run() {
		boolean[] isPrime = new boolean[1121];
		Arrays.fill(isPrime, true);
		isPrime[0] = isPrime[1] = false;
		for (int i = 2; i * i <= 1120; i++) {
			if (!isPrime[i]) continue;
			for (int j = i * 2; j <= 1120; j += i) isPrime[j] = false;
		}
		ArrayList<Integer> l = new ArrayList<Integer>();
		for (int i = 1; i <= 1120; i++) {
			if (isPrime[i]) l.add(i);
		}

		int[][] dp = new int[15][1121];
		dp[0][0] = 1;
		for (int i = 0; i < l.size(); i++) {
			for (int j = 13; j >= 0; j--) {
				for (int k = 0; k <= 1120; k++) {
					if (dp[j][k] != 0 && k + l.get(i) <= 1120) {
						dp[j + 1][k + l.get(i)] += dp[j][k];
					}
				}
			}
		}
		for (;;) {
			int n = sc.nextInt();
			int k = sc.nextInt();
			if ((n | k) == 0) return;
			System.out.println(dp[k][n]);
		}
	}

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