#include <iostream>
#include <vector>
using namespace std;

int isprime(int n){
	if(n < 2) return false;
	for(int i=2;i*i<=n;i++)
		if(n % i == 0) return false;
	return true;
}

int memo[1121][188][15];

vector<int> prime;

int dfs(int n,int pos,int k){
	
	if(k == 0) return n==0;
	if(n <= 0) return 0;
	if(pos>=188) return 0;
	if(memo[n][pos][k] != -1) return memo[n][pos][k];
	
	int ans = 0;
	for(int j=0;j<=min(1,k);j++){
		ans += dfs(n - prime[pos]*j , pos+1 , k-j);
	}
	return memo[n][pos][k] = ans;
}
int main(){
	for(int i=0;i<1121;i++)
		for(int j=0;j<188;j++)
			for(int k=0;k<15;k++)
				memo[i][j][k] = -1;
	for(int i=0;i<=1120;i++) if( isprime(i) ) prime.push_back(i);
	int a,b;
	while( cin >> a >> b && (a || b) ){
		cout << dfs(a,0,b) << endl;
	}
	
}
### Prompt

In cpp, your task is to solve 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 <vector>
using namespace std;

int isprime(int n){
	if(n < 2) return false;
	for(int i=2;i*i<=n;i++)
		if(n % i == 0) return false;
	return true;
}

int memo[1121][188][15];

vector<int> prime;

int dfs(int n,int pos,int k){
	
	if(k == 0) return n==0;
	if(n <= 0) return 0;
	if(pos>=188) return 0;
	if(memo[n][pos][k] != -1) return memo[n][pos][k];
	
	int ans = 0;
	for(int j=0;j<=min(1,k);j++){
		ans += dfs(n - prime[pos]*j , pos+1 , k-j);
	}
	return memo[n][pos][k] = ans;
}
int main(){
	for(int i=0;i<1121;i++)
		for(int j=0;j<188;j++)
			for(int k=0;k<15;k++)
				memo[i][j][k] = -1;
	for(int i=0;i<=1120;i++) if( isprime(i) ) prime.push_back(i);
	int a,b;
	while( cin >> a >> b && (a || b) ){
		cout << dfs(a,0,b) << endl;
	}
	
}
```