prithivMLmods/Coder-Stat

1 2<H1><font color="#000">Problem A:</font> And Then There Was One</H1>3 4<p>5Let’s play a stone removing game.6</p>7 8<p>9Initially, <i>n</i> stones are arranged on a circle and numbered 1, ... , <i>n</i> clockwise (Figure 1). You are also given two numbers <i>k</i> and <i>m</i>. From this state, remove stones one by one following the rules explained below, until only one remains. In step 1, remove stone <i>m</i>. In step 2, locate the <i>k</i>-th next stone clockwise from <i>m</i> and remove it. In subsequent steps, start from the slot of the stone removed in the last step, make <i>k</i> hops clockwise on the remaining stones and remove the one you reach. In other words, skip (<i>k</i> - 1) remaining stones clockwise and remove the next one. Repeat this until only one stone is left and answer its number.10</p>11<p>12For example, the answer for the case <i>n</i> = 8, <i>k</i> = 5, <i>m</i> = 3 is 1, as shown in Figure 1.13</p>14 15<center>16<img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_andThenThereWasOne">17<p>18Figure 1: An example game19</p>20</center>21 22<p>23<b>Initial state</b>: Eight stones are arranged on a circle.24</p>25<p>26<b>Step 1</b>: Stone 3 is removed since <i>m</i> = 3.27</p>28<p>29<b>Step 2</b>: You start from the slot that was occupied by stone 3. You skip four stones 4, 5, 6 and 7 (since <i>k</i> = 5), and remove the next one, which is 8.30</p>31 32<p>33<b>Step 3</b>: You skip stones 1, 2, 4 and 5, and thus remove 6. Note that you only count stones that are still on the circle and ignore those already removed. Stone 3 is ignored in this case.34</p>35 36<p>37<b>Steps 4-7</b>: You continue until only one stone is left. Notice that in later steps when only a few stones remain, the same stone may be skipped multiple times. For example, stones 1 and 4 are skipped twice in step 7.38</p>39 40<p>41<b>Final State</b>: Finally, only one stone, 1, is on the circle. This is the final state, so the answer is 1.42</p>43 44 45 46<H2>Input</H2>47 48<p>49The input consists of multiple datasets each of which is formatted as follows.50</p>51 52<pre>53<i>n k m</i>54</pre>55 56<p>57The last dataset is followed by a line containing three zeros. Numbers in a line are separated by a single space. A dataset satisfies the following conditions.58</p>59<center>60<p>61                         2 &le; <i>n</i> &le; 10000,    1 &le; <i>k</i> &le; 10000,    1 &le; <i>m</i> &le; <i>n</i>62</p>63</center>64 65<p>66The number of datasets is less than 100.67</p>68 69<H2>Output</H2>70 71<p>72For each dataset, output a line containing the stone number left in the final state. No extra characters such as spaces should appear in the output.73</p>74 75<H2>Sample Input</H2>76<pre>778 5 378100 9999 987910000 10000 10000800 0 081</pre>82 83<H2>Output for the Sample Input</H2>84<pre>851869387201988</pre>89 90 91 92 93