#include<bits/stdc++.h>
#define rep(i,n)for(int i=0;i<n;i++)
using namespace std;

bool is_prime[1121];
int prime[1121];
int dp[15][1121];

int main() {
	memset(is_prime, 1, sizeof(is_prime));
	is_prime[0] = is_prime[1] = false;
	int p = 0;
	for (int i = 2; i <= 1120; i++) {
		if (is_prime[i]) {
			prime[p++] = i;
			for (int j = i * 2; j <= 1120; j += i)is_prime[j] = false;
		}
	}
	dp[0][0] = 1;
	for (int i = 1; i <= p; i++) {
		for (int j = 14; j >= 1; j--) {
			for (int k = prime[i - 1]; k <= 1120; k++) {
				dp[j][k] += dp[j - 1][k - prime[i - 1]];
			}
		}
	}

	int n, k;
	while (scanf("%d%d", &n, &k), n)printf("%d\n", dp[k][n]);
}
### Prompt

Your challenge is to write 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<bits/stdc++.h>
#define rep(i,n)for(int i=0;i<n;i++)
using namespace std;

bool is_prime[1121];
int prime[1121];
int dp[15][1121];

int main() {
	memset(is_prime, 1, sizeof(is_prime));
	is_prime[0] = is_prime[1] = false;
	int p = 0;
	for (int i = 2; i <= 1120; i++) {
		if (is_prime[i]) {
			prime[p++] = i;
			for (int j = i * 2; j <= 1120; j += i)is_prime[j] = false;
		}
	}
	dp[0][0] = 1;
	for (int i = 1; i <= p; i++) {
		for (int j = 14; j >= 1; j--) {
			for (int k = prime[i - 1]; k <= 1120; k++) {
				dp[j][k] += dp[j - 1][k - prime[i - 1]];
			}
		}
	}

	int n, k;
	while (scanf("%d%d", &n, &k), n)printf("%d\n", dp[k][n]);
}
```