#include<stdio.h>
#include<vector>
#include<bitset>
int main()
{
	int i,j,k,d[1121][15]={0};
	std::bitset<1121>p;
	std::vector<int>v;
	for(i=2;i<1121;++i)if(!p[i])for(v.push_back(i),j=i*i;j<1121;j+=i)p[j]=1;
	for(i=0;i<v.size();++i)
	{
		for(j=13;j>=0;--j)for(k=0;k+v[i]<1121;++k)d[k+v[i]][j+1]+=d[k][j];
		++d[v[i]][1];
	}
	while(scanf("%d%d",&i,&j),i)printf("%d\n",d[i][j]);
	return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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<stdio.h>
#include<vector>
#include<bitset>
int main()
{
	int i,j,k,d[1121][15]={0};
	std::bitset<1121>p;
	std::vector<int>v;
	for(i=2;i<1121;++i)if(!p[i])for(v.push_back(i),j=i*i;j<1121;j+=i)p[j]=1;
	for(i=0;i<v.size();++i)
	{
		for(j=13;j>=0;--j)for(k=0;k+v[i]<1121;++k)d[k+v[i]][j+1]+=d[k][j];
		++d[v[i]][1];
	}
	while(scanf("%d%d",&i,&j),i)printf("%d\n",d[i][j]);
	return 0;
}
```