PAT/source/html/b1091.html

<!DOCTYPE html>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<style type="text/css">
        .katex-html {display: none;}
        .katex-mathml {font-size: 0px;}
        .katex-mathml math mrow {font-size: 16px;}
        </style>
<h1>N-自守数</h1>
<div class="ques-view"><p>如果某个数 <span class="katex"><span class="katex-mathml"><math><mrow><mi>K</mi></mrow>K</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span> 的平方乘以 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> 以后，结果的末尾几位数等于 <span class="katex"><span class="katex-mathml"><math><mrow><mi>K</mi></mrow>K</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span>，那么就称这个数为“<span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span>-自守数”。例如 <span class="katex"><span class="katex-mathml"><math><mrow><mn>3</mn><mo>×</mo><mn>9</mn><msup><mn>2</mn><mn>2</mn></msup><mo>=</mo><mn>2</mn><mn>5</mn><mn>3</mn><mn>9</mn><mn>2</mn></mrow>3\times 92^2 = 25 392</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">3</span><span class="mbin">×</span><span class="mord mathrm">9</span><span class="mord"><span class="mord mathrm">2</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mrel">=</span><span class="mord mathrm">2</span><span class="mord mathrm">5</span><span class="mord mathrm">3</span><span class="mord mathrm">9</span><span class="mord mathrm">2</span></span></span></span>，而 <span class="katex"><span class="katex-mathml"><math><mrow><mn>2</mn><mn>5</mn><mn>3</mn><mn>9</mn><mn>2</mn></mrow>25 392</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">2</span><span class="mord mathrm">5</span><span class="mord mathrm">3</span><span class="mord mathrm">9</span><span class="mord mathrm">2</span></span></span></span> 的末尾两位正好是 <span class="katex"><span class="katex-mathml"><math><mrow><mn>9</mn><mn>2</mn></mrow>92</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">9</span><span class="mord mathrm">2</span></span></span></span>，所以 <span class="katex"><span class="katex-mathml"><math><mrow><mn>9</mn><mn>2</mn></mrow>92</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">9</span><span class="mord mathrm">2</span></span></span></span> 是一个 <span class="katex"><span class="katex-mathml"><math><mrow><mn>3</mn></mrow>3</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">3</span></span></span></span>-自守数。</p>
<p>本题就请你编写程序判断一个给定的数字是否关于某个 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> 是 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span>-自守数。</p>
<h3 id="-">输入格式：</h3>
<p>输入在第一行中给出正整数 <span class="katex"><span class="katex-mathml"><math><mrow><mi>M</mi></mrow>M</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">M</span></span></span></span>（<span class="katex"><span class="katex-mathml"><math><mrow><mo>≤</mo><mn>2</mn><mn>0</mn></mrow>\le 20</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.78041em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mrel">≤</span><span class="mord mathrm">2</span><span class="mord mathrm">0</span></span></span></span>），随后一行给出 <span class="katex"><span class="katex-mathml"><math><mrow><mi>M</mi></mrow>M</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">M</span></span></span></span> 个待检测的、不超过 1000 的正整数。</p>
<h3 id="-">输出格式：</h3>
<p>对每个需要检测的数字，如果它是 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span>-自守数就在一行中输出最小的 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi><msup><mi>K</mi><mn>2</mn></msup></mrow>NK^2</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="mord"><span class="mord mathit" style="margin-right:0.07153em;">K</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> 的值，以一个空格隔开；否则输出 <code>No</code>。注意题目保证 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi><mo>&lt;</mo><mn>1</mn><mn>0</mn></mrow>N &lt; 10</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.72243em;vertical-align:-0.0391em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="mrel">&lt;</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span></span></span></span>。</p>
<h3 id="-">输入样例：</h3>
<pre><code class="lang-in">3
92 5 233
</code></pre>
<h3 id="-">输出样例：</h3>
<pre><code class="lang-out">3 25392
1 25
No
</code></pre>
</div>