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=2andk=1,theanswerisone,becausethereisonlyoneset{2}whosesumis2. Forn=1and k=1,theansweriszero. As1isnotaprime,youshouldn’tcount{1}. Forn=4andk=2,the answer is zero, because there are no sets of two different 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. Sample Input 24 3 24 2 21 11 42 18 3 17 1 17 3 17 4 100 5 1000 10 1120 14 00 Sample Output 2 3 1 0
2/2 0 2 1 0 1 55 200102899 2079324314