#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define FOR(i,a,n) for(ll i=a;i<(ll)(n);i++)

vector<int> primes(){
   vector<int> result;
   result.push_back(2);

   for(int i=2; i<1120; i++){
      for(int j=2; j<i; j++){
         if(i%j==0) break;
         if(j==i-1) result.push_back(i);
      }
   }
   return result;
}

int main(){
   vector<int> prime = primes();
   vector<vector<long>> table(14+1, vector<long>(1120+1, 0));
   table[0][0] = 1;
   for(int p : prime){
      for(int i=14; i>0; i--){
         for(int k=p; k<=1120; k++){
            table[i][k] += table[i-1][k-p];
         }
      }
   }
   
   int n,k;
   while(cin>>n>>k, n||k){
      cout << table[k][n] << 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
#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define FOR(i,a,n) for(ll i=a;i<(ll)(n);i++)

vector<int> primes(){
   vector<int> result;
   result.push_back(2);

   for(int i=2; i<1120; i++){
      for(int j=2; j<i; j++){
         if(i%j==0) break;
         if(j==i-1) result.push_back(i);
      }
   }
   return result;
}

int main(){
   vector<int> prime = primes();
   vector<vector<long>> table(14+1, vector<long>(1120+1, 0));
   table[0][0] = 1;
   for(int p : prime){
      for(int i=14; i>0; i--){
         for(int k=p; k<=1120; k++){
            table[i][k] += table[i-1][k-p];
         }
      }
   }
   
   int n,k;
   while(cin>>n>>k, n||k){
      cout << table[k][n] << endl;
   }
}


```