prithivMLmods/Coder-Stat

1 2<H1><font color="#000">Problem D:</font> Sum of Different Primes</H1>3 4<p>5A positive integer may be expressed as a sum of different prime numbers (primes), in one way or6another. Given two positive integers <i>n</i> and <i>k</i>, you should count the number of ways to express7<i>n</i> as a sum of <i>k</i> different primes. Here, two ways are considered to be the same if they sum up8the same set of the primes. For example, 8 can be expressed as 3 + 5 and 5+ 3 but they are not9distinguished.10</p>11<p>12When <i>n</i> and <i>k</i> 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 up13to 24. For <i>n</i> = 24 and <i>k</i> = 2, the answer is three, because there are three sets {5, 19}, {7,17} and {11, 13}. For <i>n</i> = 2 and <i>k</i> = 1, the answer is one, because there is only one set {2} whose14sum is 2. For <i>n</i> = 1 and <i>k</i> = 1, the answer is zero. As 1 is not a prime, you shouldn't count15{1}. For <i>n</i> = 4 and <i>k</i> = 2, the answer is zero, because there are no sets of two diffrent primes16whose sums are 4.17</p>18<p>19Your job is to write a program that reports the number of such ways for the given <i>n</i> and <i>k</i>.20</p>21 22<H2>Input</H2>23 24<p>25The input is a sequence of datasets followed by a line containing two zeros separated by a space.26A dataset is a line containing two positive integers <i>n</i> and <i>k</i> separated by a space. You may27assume that <i>n</i> &le; 1120 and <i>k</i> &le; 14.28</p>29 30<H2>Output</H2>31 32<p>33The output should be composed of lines, each corresponding to an input dataset. An output34line should contain one non-negative integer indicating the number of ways for <i>n</i> and <i>k</i> specified in the corresponding dataset. You may assume that it is less than 2<sup>31</sup>.35</p>36 37<H2>Sample Input</H2>38<pre>3924 34024 2412 1421 1434 24418 34517 14617 34717 448100 5491000 10501120 14510 052</pre>53 54<H2>Output for the Sample Input</H2>55<pre>56257358159060061262163064165556620010289967207932431468</pre>69 70 71 72 73