#include<deque>
#include<list>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<vector>
#include<algorithm>
#include<string>
#include<iostream>
#include<sstream>
#include<cmath>
#include<cstdio>
#include<cstring>
using namespace std;
int a[1120];
int er(int n){
  int i,j;
  a[0]=a[1]=0;
  for(i=2;i<n;++i)
    a[i]=i;
  for(i=2;i*i<n;++i){
    if(!a[i])
      continue;
    for(j=i*i;j<n;j+=i)
      a[j]=0;
  }
  j=2;
  for(i=0;j<n;++i){
    a[i]=a[j];
    for(j++;j<n&&a[j]==0;++j);
  }
  return i;
}
int b[15][1121][188];
int fi(int p,int q,int r){
  int i;
  if(b[p][q][r]>=0)
    return b[p][q][r];
  int sm=0;
  for(i=r;a[i]*p<=q;++i)
    sm+=fi(p-1,q-a[i],i+1);
  return b[p][q][r]=sm;
}
int main(){
  a[er(1120)]=1121;
  memset(b,-1,sizeof(b));
  memset(b,0,1121*188*sizeof(int));
  fill(b[0][0],b[0][0]+188,1);
  int n,k;
  while(cin>>n>>k,n||k)
    cout<<fi(k,n,0)<<endl;
  return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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<deque>
#include<list>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<vector>
#include<algorithm>
#include<string>
#include<iostream>
#include<sstream>
#include<cmath>
#include<cstdio>
#include<cstring>
using namespace std;
int a[1120];
int er(int n){
  int i,j;
  a[0]=a[1]=0;
  for(i=2;i<n;++i)
    a[i]=i;
  for(i=2;i*i<n;++i){
    if(!a[i])
      continue;
    for(j=i*i;j<n;j+=i)
      a[j]=0;
  }
  j=2;
  for(i=0;j<n;++i){
    a[i]=a[j];
    for(j++;j<n&&a[j]==0;++j);
  }
  return i;
}
int b[15][1121][188];
int fi(int p,int q,int r){
  int i;
  if(b[p][q][r]>=0)
    return b[p][q][r];
  int sm=0;
  for(i=r;a[i]*p<=q;++i)
    sm+=fi(p-1,q-a[i],i+1);
  return b[p][q][r]=sm;
}
int main(){
  a[er(1120)]=1121;
  memset(b,-1,sizeof(b));
  memset(b,0,1121*188*sizeof(int));
  fill(b[0][0],b[0][0]+188,1);
  int n,k;
  while(cin>>n>>k,n||k)
    cout<<fi(k,n,0)<<endl;
  return 0;
}
```