#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<cassert>
#include<iostream>
#include<sstream>
#include<string>
#include<vector>
#include<queue>
#include<set>
#include<map>
#include<utility>
#include<numeric>
#include<algorithm>
#include<bitset>
#include<complex>
#include<stack>

using namespace std;

typedef long long Int;
typedef vector<int> vint;
typedef pair<int,int> pint;
typedef vector<string> vstring;
typedef vector<pint> vpint;

struct Edge{int to,from,cost;};

#define debug cout

template<class T> void pv(T a, T b) { for (T i = a; i != b; ++i) debug << *i << " "; debug << endl; }
template<class T> void chmin(T &t, T f) { if (t > f) t = f; }
template<class T> void chmax(T &t, T f) { if (t < f) t = f; }
int in() { int x; scanf("%d", &x); return x; }

#define rep(i,n) for(int i=0;i<(n);++i)
#define repn(i,m,n) for(int i=(m);i<=(n);++i)
#define repd(i,n) for(int i=(n)-1;i>=0;--i)
#define repnd(i,m,n) for(int i=(n);i>=(m);--i)
#define rep0(i,n) for(i=0;i<(n);++i)
#define repn0(i,m,n) for(i=(m);i<=(n);++i)
#define repd0(i,n) for(i=(n)-1;i>=0;--i)
#define repnd0(i,m,n) for(i=(n);i>=(m);--i)
#define all(n) n.begin(),n.end()
#define sz(n) ((int)(n).size())
#define IL for(;;)
#define MP make_pair
#define PB push_back
#define SS stringstream
#define X second
#define Y first
#define PUTLINE debug<<"LINE:"<<__LINE__<<endl;

const int INF = 2147483647/3;
const double EPS = 1e-10;
const double PI = acos(-1.0);

const int dx[]={1,-1,0,0,1,-1,1,-1,0};
const int dy[]={0,0,1,-1,1,-1,-1,1,0};

vint prime;
int mem[1121][15][305];

int f(int n,int k,int m){
	if(mem[n][k][m]>=0)return mem[n][k][m];
	if(k==0){
		if(n==0){
			return 1;
		}else{
			return 0;
		}
	}
	Int res=0;
	for(int i=0;i<m&&prime[i]<=n;++i){
		res+=f(n-prime[i],k-1,i);
	}
	mem[n][k][m]=res;
	return res;
}

int main() {
	repn(i,2,2000){
		int j;
		repn0(j,2,i-1)if(i%j==0)break;
		if(i==j)prime.PB(i);
	}
	memset(mem,-1,sizeof(mem));
	int n,k;
	IL{
		cin>>n>>k;
		if(n==0&&k==0)break;
		int m;
		rep0(m,305)if(prime[m]>n)break;
		cout<<f(n,k,m)<<endl;
	}
	return 0;
}
### 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<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<cassert>
#include<iostream>
#include<sstream>
#include<string>
#include<vector>
#include<queue>
#include<set>
#include<map>
#include<utility>
#include<numeric>
#include<algorithm>
#include<bitset>
#include<complex>
#include<stack>

using namespace std;

typedef long long Int;
typedef vector<int> vint;
typedef pair<int,int> pint;
typedef vector<string> vstring;
typedef vector<pint> vpint;

struct Edge{int to,from,cost;};

#define debug cout

template<class T> void pv(T a, T b) { for (T i = a; i != b; ++i) debug << *i << " "; debug << endl; }
template<class T> void chmin(T &t, T f) { if (t > f) t = f; }
template<class T> void chmax(T &t, T f) { if (t < f) t = f; }
int in() { int x; scanf("%d", &x); return x; }

#define rep(i,n) for(int i=0;i<(n);++i)
#define repn(i,m,n) for(int i=(m);i<=(n);++i)
#define repd(i,n) for(int i=(n)-1;i>=0;--i)
#define repnd(i,m,n) for(int i=(n);i>=(m);--i)
#define rep0(i,n) for(i=0;i<(n);++i)
#define repn0(i,m,n) for(i=(m);i<=(n);++i)
#define repd0(i,n) for(i=(n)-1;i>=0;--i)
#define repnd0(i,m,n) for(i=(n);i>=(m);--i)
#define all(n) n.begin(),n.end()
#define sz(n) ((int)(n).size())
#define IL for(;;)
#define MP make_pair
#define PB push_back
#define SS stringstream
#define X second
#define Y first
#define PUTLINE debug<<"LINE:"<<__LINE__<<endl;

const int INF = 2147483647/3;
const double EPS = 1e-10;
const double PI = acos(-1.0);

const int dx[]={1,-1,0,0,1,-1,1,-1,0};
const int dy[]={0,0,1,-1,1,-1,-1,1,0};

vint prime;
int mem[1121][15][305];

int f(int n,int k,int m){
	if(mem[n][k][m]>=0)return mem[n][k][m];
	if(k==0){
		if(n==0){
			return 1;
		}else{
			return 0;
		}
	}
	Int res=0;
	for(int i=0;i<m&&prime[i]<=n;++i){
		res+=f(n-prime[i],k-1,i);
	}
	mem[n][k][m]=res;
	return res;
}

int main() {
	repn(i,2,2000){
		int j;
		repn0(j,2,i-1)if(i%j==0)break;
		if(i==j)prime.PB(i);
	}
	memset(mem,-1,sizeof(mem));
	int n,k;
	IL{
		cin>>n>>k;
		if(n==0&&k==0)break;
		int m;
		rep0(m,305)if(prime[m]>n)break;
		cout<<f(n,k,m)<<endl;
	}
	return 0;
}
```