prithivMLmods/Coder-Stat

1 2<H1><font color="#000">Problem A: </font>Equal Sum Sets</H1>3 4<p>5Let us consider sets of positive integers less than or equal to <var>n</var>. Note that all elements of a set are different. Also note that the order of elements doesn't matter, that is, both {3, 5, 9} and {5, 9, 3} mean the same set.6</p>7 8<p>9Specifying the number of set elements and their sum to be <var>k</var> and <var>s</var>, respectively, sets satisfying the conditions are limited. When <var>n</var> = 9, <var>k</var> = 3 and <var>s</var> = 23, {6, 8, 9} is the only such set. There may be more than one such set, in general, however. When <var>n</var> = 9, <var>k</var> = 3 and <var>s</var> = 22, both {5, 8, 9} and {6, 7, 9} are possible.10</p>11 12<p>13You have to write a program that calculates the number of the sets that satisfy the given conditions.14</p>15 16<H2>Input</H2>17 18<p>19The input consists of multiple datasets. The number of datasets does not exceed 100.20</p>21 22<p>23Each of the datasets has three integers <var>n</var>, <var>k</var> and <var>s</var> in one line, separated by a space. You may assume 1 &le; <var>n</var> &le; 20, 1 &le; <var>k</var> &le; 10 and 1 &le; <var>s</var> &le; 155.24</p>25 26<p>27The end of the input is indicated by a line containing three zeros. 28</p>29 30<H2>Output</H2>31 32<p>33The output for each dataset should be a line containing a single integer that gives the number of the sets that satisfy the conditions. No other characters should appear in the output.34</p>35 36<p>37You can assume that the number of sets does not exceed 2<sup>31</sup> - 1.38</p>39 40<H2>Sample Input</H2>41<pre>429 3 23439 3 224410 3 284516 10 1074620 8 1024720 10 1054820 10 155493 4 3504 2 11510 0 052</pre>53 54<H2>Output for the Sample Input</H2>55<pre>561572580592060154261544862163064065</pre>