#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

vector<int> pn;
vector<bool> is_p;

void enum_prime()
{
  is_p.resize(1515, true);
  is_p[0] = is_p[1] = false;
  for(int i = 2; i <= 1515; i++) {
    if(!is_p[i]) continue;
    pn.push_back(i);
    for(int j = i+i; j <= 1515; j+=i) is_p[j] = false;
  }
}

int dp[1200][300][15];

int solve(int n, int p, int k)
{
  if(k == 0 && n == 0) return 1;
  if(k < 0 || n < 0 || p < 0) return 0;  
  
  int& ret = dp[n][p][k];
  if(~ret) return ret;

  ret = solve(n, p - 1, k);
  if(n >= pn[p]) ret += solve(n - pn[p], p - 1, k - 1);

  return ret;
}

int main()
{
  enum_prime();
  int n, k;
  while(cin >> n >> k, n || k) {
    memset(dp, -1, sizeof(dp));
    int p = upper_bound(pn.begin(), pn.end(), n) - pn.begin() - 1;
    cout << solve(n, p, k) << endl;
  }
  return 0;
}
### 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 <bits/stdc++.h>

using namespace std;

typedef long long ll;

vector<int> pn;
vector<bool> is_p;

void enum_prime()
{
  is_p.resize(1515, true);
  is_p[0] = is_p[1] = false;
  for(int i = 2; i <= 1515; i++) {
    if(!is_p[i]) continue;
    pn.push_back(i);
    for(int j = i+i; j <= 1515; j+=i) is_p[j] = false;
  }
}

int dp[1200][300][15];

int solve(int n, int p, int k)
{
  if(k == 0 && n == 0) return 1;
  if(k < 0 || n < 0 || p < 0) return 0;  
  
  int& ret = dp[n][p][k];
  if(~ret) return ret;

  ret = solve(n, p - 1, k);
  if(n >= pn[p]) ret += solve(n - pn[p], p - 1, k - 1);

  return ret;
}

int main()
{
  enum_prime();
  int n, k;
  while(cin >> n >> k, n || k) {
    memset(dp, -1, sizeof(dp));
    int p = upper_bound(pn.begin(), pn.end(), n) - pn.begin() - 1;
    cout << solve(n, p, k) << endl;
  }
  return 0;
}
```