#include <iostream>
#include <cstring>

using namespace std;

int main(){
  int prime[187];
  static int memo[1121][187][15];
  memset(memo, 0, sizeof(memo));
  int size = 1;
  prime[0] = 2;
  for(int i=3;i<1120;i+=2){
    bool flag = true;
    for(int j=0;prime[j]*prime[j]<=i;j++)
      if(i%prime[j]==0) flag = false;
    if(flag) prime[size++] = i;
  }
  for(int i=0;i<size;i++) memo[prime[i]][i][1] = 1;
  for(int i=1;i<14;i++){
    for(int j=0;j<1121;j++){
      for(int k=0;k<187;k++){
	if(memo[j][k][i]==0) continue;
	for(int l=k+1;l<187;l++){
	  if(j+prime[l]>1120) break;
	  memo[j+prime[l]][l][i+1] += memo[j][k][i];
	}
      }
    }
  }
  int n, k;
  while(cin >> n >> k, n){
    int ans = 0;
    for(int i=0;i<187;i++) ans += memo[n][i][k];
    printf("%d\n", ans);
  }
}
### 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 <cstring>

using namespace std;

int main(){
  int prime[187];
  static int memo[1121][187][15];
  memset(memo, 0, sizeof(memo));
  int size = 1;
  prime[0] = 2;
  for(int i=3;i<1120;i+=2){
    bool flag = true;
    for(int j=0;prime[j]*prime[j]<=i;j++)
      if(i%prime[j]==0) flag = false;
    if(flag) prime[size++] = i;
  }
  for(int i=0;i<size;i++) memo[prime[i]][i][1] = 1;
  for(int i=1;i<14;i++){
    for(int j=0;j<1121;j++){
      for(int k=0;k<187;k++){
	if(memo[j][k][i]==0) continue;
	for(int l=k+1;l<187;l++){
	  if(j+prime[l]>1120) break;
	  memo[j+prime[l]][l][i+1] += memo[j][k][i];
	}
      }
    }
  }
  int n, k;
  while(cin >> n >> k, n){
    int ans = 0;
    for(int i=0;i<187;i++) ans += memo[n][i][k];
    printf("%d\n", ans);
  }
}
```