#include<iostream>
#include<vector>
using namespace std;

int n,m;
int dp[2000][20];
vector<int> pv;

int main(){
  for(int i=2;i<=1120;i++){
    bool f = true;
    for(int j=2;j*j<=i;j++){
      if(i%j==0){
	f = false;
	break;
      }
    }
    if(f)pv.push_back(i);
  }

  for(int i=0;i<=1120;i++)
    for(int j=0;j<=14;j++)dp[i][j] = 0;
  dp[0][0] = 1;

  for(int k=0;k<pv.size();k++){
    for(int i=1120;i>=0;i--){
      for(int j=13;j>=0;j--){
	if(i+pv[k]<=1120)dp[i+pv[k]][j+1] += dp[i][j];
      }
    }
  }

  while(cin >> n >> m,n||m){
    cout << dp[n][m] << endl;
  }
}
### 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<vector>
using namespace std;

int n,m;
int dp[2000][20];
vector<int> pv;

int main(){
  for(int i=2;i<=1120;i++){
    bool f = true;
    for(int j=2;j*j<=i;j++){
      if(i%j==0){
	f = false;
	break;
      }
    }
    if(f)pv.push_back(i);
  }

  for(int i=0;i<=1120;i++)
    for(int j=0;j<=14;j++)dp[i][j] = 0;
  dp[0][0] = 1;

  for(int k=0;k<pv.size();k++){
    for(int i=1120;i>=0;i--){
      for(int j=13;j>=0;j--){
	if(i+pv[k]<=1120)dp[i+pv[k]][j+1] += dp[i][j];
      }
    }
  }

  while(cin >> n >> m,n||m){
    cout << dp[n][m] << endl;
  }
}
```