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

int N, K;
int f[1121][15];
vector< int > prime;

void preprocess(void);

int main() {
  preprocess();
  while (cin >> N >> K, N + K)
    cout << f[N][K] << "\n";

  return 0;
}

void preprocess(void) {
  static bool is_prime[1120];

  prime.push_back(2);
  fill(&is_prime[0], &is_prime[1120], true);
  for (int i = 3; i < 1120; i += 2)
    if (is_prime[i]) {
      prime.push_back(i);
      for (int j = i; i * j < 1120; ++j)
        is_prime[i * j] = false;
    }

  f[0][0] = 1;
  for (int p = 0; p < prime.size(); ++p)
    for (int i = 1120 - prime[p]; i >= 0; --i)
      for (int j = 13; j >= 0; --j)
        f[i + prime[p]][j + 1] += f[i][j];
}
### 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 <iostream>
#include <algorithm>
#include <vector>
using namespace std;

int N, K;
int f[1121][15];
vector< int > prime;

void preprocess(void);

int main() {
  preprocess();
  while (cin >> N >> K, N + K)
    cout << f[N][K] << "\n";

  return 0;
}

void preprocess(void) {
  static bool is_prime[1120];

  prime.push_back(2);
  fill(&is_prime[0], &is_prime[1120], true);
  for (int i = 3; i < 1120; i += 2)
    if (is_prime[i]) {
      prime.push_back(i);
      for (int j = i; i * j < 1120; ++j)
        is_prime[i * j] = false;
    }

  f[0][0] = 1;
  for (int p = 0; p < prime.size(); ++p)
    for (int i = 1120 - prime[p]; i >= 0; --i)
      for (int j = 13; j >= 0; --j)
        f[i + prime[p]][j + 1] += f[i][j];
}
```