#include<iostream>
#include<algorithm>
#include<vector>
#include<cmath>
#define rep(i,n) for(int i=0;i<n;i++)
#define MAX 1121
using namespace std;
typedef pair<int,int> P;
bool isntprime[MAX+1];
vector<int> prime;
int dp[MAX+1][16];

int main()
{

  isntprime[0] = isntprime[1] = true;
  int j;
  for(int i=2;i<=MAX;i++)if(!isntprime[i])for(prime.push_back(i),j=2*i;j<=1120;j+=i)isntprime[j] = true;
  int psize = prime.size();

  rep(i,MAX)rep(k,16)dp[i][k]=0;
  dp[0][0] = 1;

  rep(i,psize)
    {
      for(int j=14;j>=0;j--)
	{
	  rep(k,1121)
	    {
	      if(dp[k][j] == 0)continue;
	      if(k+prime[i] > 1120)continue;
	      dp[k+prime[i]][j+1] += dp[k][j];
	    }
	}
    }

  int n,k;
  while(cin >> n >> k,n|k)
    cout << dp[n][k] << endl;
    
  return 0;
}
### Prompt

Generate a cpp solution to the following problem:

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<iostream>
#include<algorithm>
#include<vector>
#include<cmath>
#define rep(i,n) for(int i=0;i<n;i++)
#define MAX 1121
using namespace std;
typedef pair<int,int> P;
bool isntprime[MAX+1];
vector<int> prime;
int dp[MAX+1][16];

int main()
{

  isntprime[0] = isntprime[1] = true;
  int j;
  for(int i=2;i<=MAX;i++)if(!isntprime[i])for(prime.push_back(i),j=2*i;j<=1120;j+=i)isntprime[j] = true;
  int psize = prime.size();

  rep(i,MAX)rep(k,16)dp[i][k]=0;
  dp[0][0] = 1;

  rep(i,psize)
    {
      for(int j=14;j>=0;j--)
	{
	  rep(k,1121)
	    {
	      if(dp[k][j] == 0)continue;
	      if(k+prime[i] > 1120)continue;
	      dp[k+prime[i]][j+1] += dp[k][j];
	    }
	}
    }

  int n,k;
  while(cin >> n >> k,n|k)
    cout << dp[n][k] << endl;
    
  return 0;
}
```