#include <iostream>
#include <sstream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
#include <numeric>
#include <climits>
#include <cfloat>
using namespace std;

void primeNumber(int N, vector<bool>& prime)
{
    prime.assign(N+1, true);
    prime [0] = prime[1] = false;
    for(int i=2; i*i<=N; i++){
        if(prime[i]){
            for(int j=i; i*j<=N; j++){
                prime[i*j] = false;
            }
        }
    }
}

int main()
{
    vector<bool> prime;
    primeNumber(1120, prime);

    for(;;){
        int n, m;
        cin >> n >> m;
        if(n == 0)
            return 0;

        vector<vector<int> > dp(m+1, vector<int>(n+1, 0));
        dp[0][0] = 1;
        for(int i=0; i<=n; ++i){
            if(!prime[i])
                continue;
            for(int j=m-1; j>=0; --j){
                for(int k=i; k<=n; ++k){
                    dp[j+1][k] += dp[j][k-i];
                }
            }
        }

        cout << dp[m][n] << endl;
    }
}
### Prompt

Your challenge is to write 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 <sstream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
#include <numeric>
#include <climits>
#include <cfloat>
using namespace std;

void primeNumber(int N, vector<bool>& prime)
{
    prime.assign(N+1, true);
    prime [0] = prime[1] = false;
    for(int i=2; i*i<=N; i++){
        if(prime[i]){
            for(int j=i; i*j<=N; j++){
                prime[i*j] = false;
            }
        }
    }
}

int main()
{
    vector<bool> prime;
    primeNumber(1120, prime);

    for(;;){
        int n, m;
        cin >> n >> m;
        if(n == 0)
            return 0;

        vector<vector<int> > dp(m+1, vector<int>(n+1, 0));
        dp[0][0] = 1;
        for(int i=0; i<=n; ++i){
            if(!prime[i])
                continue;
            for(int j=m-1; j>=0; --j){
                for(int k=i; k<=n; ++k){
                    dp[j+1][k] += dp[j][k-i];
                }
            }
        }

        cout << dp[m][n] << endl;
    }
}
```