prithivMLmods/Coder-Stat

1 2<h3>Integral Rectangles</h3>3 4<p>5Let us consider rectangles whose height, <i>h</i>, and6width, <i>w</i>, are both integers. We call such rectangles <em>7integral rectangles</em>. In this problem, we consider only wide8integral rectangles, i.e., those with <i>w</i> &gt; <i>h</i>.9</p>10 11<p>12We define the following ordering of wide integral rectangles. Given13two wide integral rectangles,14</p>15 16<ol>17<li>18The one shorter in its diagonal line is smaller, and19</li>20<li>21If the two have diagonal lines with the same length, the one shorter22 in its height is smaller.23</li>24</ol>25 26 27<center>28<img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE2_integralRectangles-en">29</center>30 31 32<p>33Given a wide integral rectangle, find the smallest wide integral34rectangle bigger than the given one.35</p>36 37 38<h3>Input</h3>39 40<p>The entire input consists of multiple datasets. The number of41 datasets is no more than 100. Each dataset describes a wide integral42 rectangle by specifying its height and width, namely <i>h</i>43 and <i>w</i>, separated by a space in a line, as follows.44</p>45 46<blockquote>47<i>h</i> <i>w</i>48</blockquote>49 50 51<p>52For each dataset, <i>h</i> and <i>w</i> (&gt;<i>h</i>) are both53integers greater than 0 and no more than 100. 54</p>55 56<p>57The end of the input is indicated by a line of two zeros separated by a space.58</p>59 60 61<h3>Output</h3>62 63<p>64For each dataset, print in a line two numbers describing the65height and width, namely <i>h</i> and <i>w</i> (&gt; <i>h</i>), of the66smallest wide integral rectangle bigger than the one described in the67dataset.  Put a space between the numbers. No other68characters are allowed in the output.69</p>70 71<p>72For any wide integral rectangle given in the input, the width and73height of the smallest wide integral rectangle bigger than the given74one are both known to be not greater than 150. 75</p>76<p>77In addition, although78the ordering of wide integral rectangles uses the comparison of79lengths of diagonal lines, this comparison can be replaced with that80of squares (self-products) of lengths of diagonal lines, which can81avoid unnecessary troubles possibly caused by the use of floating-point82numbers.83</p>84 85 86<h3>Sample Input</h3>87<pre>881 2891 3902 3911 4922 4935 6941 8954 79698 1009799 100980 099</pre>100 101 102<h3>Output for the Sample Input</h3>103 104<pre>1051 31062 31071 41082 41093 41101 81114 71122 81133 14011489 109115</pre>116