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.*;
import java.awt.geom.*;
import java.io.*;
public class Main{
	int [][] dp;
	int MAX = 1120;
	int K= 14;
	boolean [] isprime;
	
	private void doit(){
		Scanner sc = new Scanner(System.in);
		
		isprime = new boolean[MAX + 1];
		eratos();
		
		dp = new int[K + 1][MAX + 1];
		dp();
		while(true){
			int n = sc.nextInt();
			int k = sc.nextInt();
			if((n|k) == 0) break;
			int ans = dp[k][n];
			//System.out.print("ANS = ");
			System.out.println(ans);
		}
		//debug
//		for(int i = 0; i < 30; i++){
//			System.out.println("i = " + i + "value= " + dp[1][i] + " "+ dp[2][i] + " dp3 = " + dp[3][i] + " dp4 = " + dp[4][i]);
//		}
	}

	private void dp() {
		//init
		for(int i = 1; i <= MAX; i++){
			dp[1][i] = isprime[i] ? 1 : 0;
		}
		
		for(int i = MAX; i >= 2; i--){
			if(! isprime[i]) continue;
			//for(int j = i; j <= MAX; j++){
			for(int j = MAX; j >= i; j--){
				for(int k = K - 1; k  >= 1; k--){
					if(k == 1 && j == i) continue;
					if(j + i > MAX) continue;
					dp[k+1][j + i] += dp[k][j];
//					if(j + i == 8 && k == 2){
//						System.out.println("debug=  " + i + " " + j  + " " + k + " " + dp[k][j]);
//					}
				}
			}
			
//			for(int j = i; j >= 2; j--){
//			for(int k = 1; k < K; k++){
//				if(k == 1 && j == i) continue;
//				if(j + i > MAX) continue;
//				dp[k + 1][j + i] += dp[k][j]; 
//				if(k == 2 && j == 5 && i == 5){
//					System.out.println("test");
//					System.out.println((j + i) + " " + dp[k][j]);
//				}
//			}
//		}
			// 2, 3 , 5
			//[0][5] => [1][5] = 1にする
			//[2][5] => [3][5 + 5] = 1にする
		}
	}

	private void eratos() {
		Arrays.fill(isprime, true);
		isprime[0] = false;
		isprime[1] = false;
		for(int i = 2; i * i <= MAX; i++){
			if(isprime[i]){
				for(int j = i * 2; j <= MAX; j+= i){
					isprime[j] = false;
				}
			}
		}
		
	}

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