#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <iostream>
#include <vector>
#include <string>
#include <sstream>
#include <algorithm>
#include <utility>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <deque>
#include <functional>

using namespace std;

#define fst first
#define scd second
#define PB push_back
#define MP make_pair
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define omajinai ios::sync_with_stdio(false);cin.tie(0)
#define rep(i,x) for(int i=0;i<(int)(x);++i)
#define rep1(i,x) for(int i=1;i<=(int)(x);++i)

using ll=long long;
using ld=long double;
using vi=vector<int>;
using vvi=vector<vi>;
using pii=pair<int, int>;
using vpii=vector<pii>;

template<class T,class U>ostream&operator<<(ostream&os,const pair<T,U>p){os<<"("<<p.fst<<", "<<p.scd<<")";return os;}
template<class T>ostream&operator<<(ostream&os,const vector<T>v){rep(i,v.size()){if(i)os<<", ";os<<v[i];}return os;}
template<typename T>T&max(T&a,T&b){if(a>=b)return a;return b;}
template<typename T>T&min(T&a,T&b){if(a < b)return a;return b;}
template<typename T>bool chmax(T&a,T b){if(a < b){a=b;return true;}return false;}
template<typename T>bool chmin(T&a,T b){if(a > b){a=b;return true;}return false;}

constexpr int inf = 1e9;
constexpr ll linf = 3e18;
constexpr double eps = 1e-9;

int dp[15][1125];
vi primes;

void sieve()
{
    bool p[1301];

    rep(i, 1301) p[i] = true;

    p[0] = p[1] = false;

    for (int i = 2; i <= 1300; ++i) {
        if (!p[i]) continue;

        for (int j = i + i; j <= 1300; j += i) {
            p[j] = false;
        }
    }

    for (int i = 2; i <= 1125; ++i) if (p[i]) {
        primes.PB(i);
    }
}

int main()
{
    sieve();

    dp[0][0] = 1;

    for (int i = 0; i < primes.size(); ++i) {
        for (int j = 14; j >= 1; --j) {
            for (int k = 0; k <= 1120; ++k) {
                if (k - primes[i] >= 0) dp[j][k] += dp[j - 1][k - primes[i]];
            }
        }
    }

    int n, k;

    while (cin >> n >> k, n && k) {
        cout << dp[k][n] << endl;
    }
}
### Prompt

Create a solution in cpp for 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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <iostream>
#include <vector>
#include <string>
#include <sstream>
#include <algorithm>
#include <utility>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <deque>
#include <functional>

using namespace std;

#define fst first
#define scd second
#define PB push_back
#define MP make_pair
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define omajinai ios::sync_with_stdio(false);cin.tie(0)
#define rep(i,x) for(int i=0;i<(int)(x);++i)
#define rep1(i,x) for(int i=1;i<=(int)(x);++i)

using ll=long long;
using ld=long double;
using vi=vector<int>;
using vvi=vector<vi>;
using pii=pair<int, int>;
using vpii=vector<pii>;

template<class T,class U>ostream&operator<<(ostream&os,const pair<T,U>p){os<<"("<<p.fst<<", "<<p.scd<<")";return os;}
template<class T>ostream&operator<<(ostream&os,const vector<T>v){rep(i,v.size()){if(i)os<<", ";os<<v[i];}return os;}
template<typename T>T&max(T&a,T&b){if(a>=b)return a;return b;}
template<typename T>T&min(T&a,T&b){if(a < b)return a;return b;}
template<typename T>bool chmax(T&a,T b){if(a < b){a=b;return true;}return false;}
template<typename T>bool chmin(T&a,T b){if(a > b){a=b;return true;}return false;}

constexpr int inf = 1e9;
constexpr ll linf = 3e18;
constexpr double eps = 1e-9;

int dp[15][1125];
vi primes;

void sieve()
{
    bool p[1301];

    rep(i, 1301) p[i] = true;

    p[0] = p[1] = false;

    for (int i = 2; i <= 1300; ++i) {
        if (!p[i]) continue;

        for (int j = i + i; j <= 1300; j += i) {
            p[j] = false;
        }
    }

    for (int i = 2; i <= 1125; ++i) if (p[i]) {
        primes.PB(i);
    }
}

int main()
{
    sieve();

    dp[0][0] = 1;

    for (int i = 0; i < primes.size(); ++i) {
        for (int j = 14; j >= 1; --j) {
            for (int k = 0; k <= 1120; ++k) {
                if (k - primes[i] >= 0) dp[j][k] += dp[j - 1][k - primes[i]];
            }
        }
    }

    int n, k;

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