#include<cstdio>
#include<vector>

#define	pb			push_back
#define	rep(i,n)	for(int i=0;i<n;i++)

using namespace std;

typedef	vector<int>	vi;

int main(){
	const int Ne=1200;
	static bool er[Ne]; er[0]=er[1]=true;
	for(int i=2;i*i<Ne;i++) if(!er[i]) for(int j=i*i;j<Ne;j+=i) er[j]=true;
	vi p; rep(i,Ne) if(!er[i]) p.pb(i);

	static int cnt[15][1121];	cnt[0][0]=1;
	rep(i,p.size()){
		for(int k=min(i+1,14);k>=1;k--){
			for(int j=p[i];j<=1120;j++){
				if(cnt[k-1][j-p[i]]>0)	cnt[k][j]+=cnt[k-1][j-p[i]];
			}
		}
	}

	for(int n,k;scanf("%d%d",&n,&k),n;)	printf("%d\n",cnt[k][n]);

	return 0;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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

### Response

```cpp
#include<cstdio>
#include<vector>

#define	pb			push_back
#define	rep(i,n)	for(int i=0;i<n;i++)

using namespace std;

typedef	vector<int>	vi;

int main(){
	const int Ne=1200;
	static bool er[Ne]; er[0]=er[1]=true;
	for(int i=2;i*i<Ne;i++) if(!er[i]) for(int j=i*i;j<Ne;j+=i) er[j]=true;
	vi p; rep(i,Ne) if(!er[i]) p.pb(i);

	static int cnt[15][1121];	cnt[0][0]=1;
	rep(i,p.size()){
		for(int k=min(i+1,14);k>=1;k--){
			for(int j=p[i];j<=1120;j++){
				if(cnt[k-1][j-p[i]]>0)	cnt[k][j]+=cnt[k-1][j-p[i]];
			}
		}
	}

	for(int n,k;scanf("%d%d",&n,&k),n;)	printf("%d\n",cnt[k][n]);

	return 0;
}
```