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

const int MAX_N = 1120;
const int MAX_K = 14;

vector<int> sieve(int n) {
	vector<int> res(1, 2);
	vector<bool> prime(n, true);
	for(int i = 3; i < n; i += 2) {
		if(prime[i]) {
			res.push_back(i);
			for(long long j = static_cast<long long>(i) * i; j < n; j += i * 2)
				prime[j] = false;
		}
	}

	return res;
}

int main() {
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	const auto primes = sieve(MAX_N + 1);
	const int num = primes.size();

	array<array<int, MAX_K + 1>, MAX_N + 1> dp{};
	dp[0][0] = 1;

	for(int i = 0; i < num; ++i) {
		for(int j = MAX_N - primes[i]; j >= 0; --j) {
			for(int l = MAX_K - 1; l >= 0; --l) {
				dp[j + primes[i]][l + 1] += dp[j][l];
			}
		}
	}

	for(int n, k; cin >> n >> k && n;) {
		cout << dp[n][k] << endl;
	}

	return EXIT_SUCCESS;
}
### 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 <array>
#include <cstdlib>
#include <iostream>
#include <vector>
using namespace std;

const int MAX_N = 1120;
const int MAX_K = 14;

vector<int> sieve(int n) {
	vector<int> res(1, 2);
	vector<bool> prime(n, true);
	for(int i = 3; i < n; i += 2) {
		if(prime[i]) {
			res.push_back(i);
			for(long long j = static_cast<long long>(i) * i; j < n; j += i * 2)
				prime[j] = false;
		}
	}

	return res;
}

int main() {
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	const auto primes = sieve(MAX_N + 1);
	const int num = primes.size();

	array<array<int, MAX_K + 1>, MAX_N + 1> dp{};
	dp[0][0] = 1;

	for(int i = 0; i < num; ++i) {
		for(int j = MAX_N - primes[i]; j >= 0; --j) {
			for(int l = MAX_K - 1; l >= 0; --l) {
				dp[j + primes[i]][l + 1] += dp[j][l];
			}
		}
	}

	for(int n, k; cin >> n >> k && n;) {
		cout << dp[n][k] << endl;
	}

	return EXIT_SUCCESS;
}
```