#include <iostream>
#include <vector>

using namespace std;

#define MAX_N 1121
#define MAX_K 15
typedef long long ll;
 
bool prime[MAX_N];
ll dp[MAX_N][MAX_K];
 
void Prime(){
    fill(prime,prime+MAX_N,true);
    prime[0] = prime[1] = false;
 
    for(int i = 2 ; i*i < MAX_N ; i++){
	if(prime[i]){
	    for(int j = i*i ; j < MAX_N ; j += i){
		prime[j] = false;
	    }
	}
    }
}
 
void init(){
    Prime();
    vector<int> P;
    for(int i = 0 ; i < MAX_N ; i++){
	if(prime[i]){
	    P.push_back(i);
	}
    }
 
    dp[0][0] = 1;
    for(int i = 0 ; i < (int)P.size() ; i++){
	for(int j = MAX_K-2 ; j >= 0 ; j--){
	    for(int k = 0 ; k < MAX_N-P[i] ; k++){
		dp[P[i]+k][j+1] += dp[k][j];
	    }
	}
    }
}
 
int main(){
    int n,k;
 
    init();
    while(cin >> n >> k, n | k){
	cout << dp[n][k] << endl;
    }
    return 0;
}
### Prompt

Your task is to create 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 <vector>

using namespace std;

#define MAX_N 1121
#define MAX_K 15
typedef long long ll;
 
bool prime[MAX_N];
ll dp[MAX_N][MAX_K];
 
void Prime(){
    fill(prime,prime+MAX_N,true);
    prime[0] = prime[1] = false;
 
    for(int i = 2 ; i*i < MAX_N ; i++){
	if(prime[i]){
	    for(int j = i*i ; j < MAX_N ; j += i){
		prime[j] = false;
	    }
	}
    }
}
 
void init(){
    Prime();
    vector<int> P;
    for(int i = 0 ; i < MAX_N ; i++){
	if(prime[i]){
	    P.push_back(i);
	}
    }
 
    dp[0][0] = 1;
    for(int i = 0 ; i < (int)P.size() ; i++){
	for(int j = MAX_K-2 ; j >= 0 ; j--){
	    for(int k = 0 ; k < MAX_N-P[i] ; k++){
		dp[P[i]+k][j+1] += dp[k][j];
	    }
	}
    }
}
 
int main(){
    int n,k;
 
    init();
    while(cin >> n >> k, n | k){
	cout << dp[n][k] << endl;
    }
    return 0;
}
```