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24 lines
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24 lines
3.5 KiB
HTML
Radix
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<div class="ques-view"><p>Given a pair of positive integers, for example, 6 and 110, can this equation 6 = 110 be true? The answer is <code>yes</code>, if 6 is a decimal number and 110 is a binary number.</p>
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<p>Now for any pair of positive integers <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mn>1</mn></msub></mrow>N_1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</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> and <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mn>2</mn></msub></mrow>N_2</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped 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>, your task is to find the radix of one number while that of the other is given.</p>
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<h3 id="input-specification-">Input Specification:</h3>
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<p>Each input file contains one test case. Each case occupies a line which contains 4 positive integers:</p>
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<pre><code>
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N1 N2 tag radix
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</code></pre><p>Here <code>N1</code> and <code>N2</code> each has no more than 10 digits. A digit is less than its radix and is chosen from the set { 0-9, <code>a</code>-<code>z</code> } where 0-9 represent the decimal numbers 0-9, and <code>a</code>-<code>z</code> represent the decimal numbers 10-35. The last number <code>radix</code> is the radix of <code>N1</code> if <code>tag</code> is 1, or of <code>N2</code> if <code>tag</code> is 2.</p>
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<h3 id="output-specification-">Output Specification:</h3>
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<p>For each test case, print in one line the radix of the other number so that the equation <code>N1</code> = <code>N2</code> is true. If the equation is impossible, print <code>Impossible</code>. If the solution is not unique, output the smallest possible radix.</p>
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<h3 id="sample-input-1-">Sample Input 1:</h3>
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<pre><code class="lang-in">6 110 1 10
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</code></pre>
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<h3 id="sample-output-1-">Sample Output 1:</h3>
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<pre><code class="lang-out">2
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</code></pre>
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<h3 id="sample-input-2-">Sample Input 2:</h3>
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<pre><code class="lang-in">1 ab 1 2
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</code></pre>
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<h3 id="sample-output-2-">Sample Output 2:</h3>
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<pre><code class="lang-out">Impossible
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</code></pre>
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</div> |