PAT/source/html/a1037.html

Magic Coupon
<div class="ques-view"><p>The magic shop in Mars is offering some magic coupons. Each coupon has an integer <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> printed on it, meaning that when you use this coupon with a product, you may get <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> times the value of that product back! What is more, the shop also offers some bonus product for free. However, if you apply a coupon with a positive <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> to this bonus product, you will have to pay the shop <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> times the value of the bonus product... but hey, magically, they have some coupons with negative <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>'s!</p>
<p>For example, given a set of coupons { 1 2 4 <span class="katex"><span class="katex-mathml"><math><mrow><mo>−</mo><mn>1</mn></mrow>-1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord">−</span><span class="mord mathrm">1</span></span></span></span> }, and a set of product values { 7 6 <span class="katex"><span class="katex-mathml"><math><mrow><mo>−</mo><mn>2</mn></mrow>-2</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord">−</span><span class="mord mathrm">2</span></span></span></span> <span class="katex"><span class="katex-mathml"><math><mrow><mo>−</mo><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:0.72777em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord">−</span><span class="mord mathrm">3</span></span></span></span> } (in Mars dollars M$) where a negative value corresponds to a bonus product. You can apply coupon 3 (with <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> being 4) to product 1 (with value M$7) to get M$28 back; coupon 2 to product 2 to get M$12 back; and coupon 4 to product 4 to get M$3 back. On the other hand, if you apply coupon 3 to product 4, you will have to pay M$12 to the shop.</p>
<p>Each coupon and each product may be selected at most once. Your task is to get as much money back as possible.</p>
<h3 id="input-specification-">Input Specification:</h3>
<p>Each input file contains one test case. For each case, the first line contains the number of coupons <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mi>C</mi></msub></mrow>N_C</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 mathit mtight" style="margin-right:0.07153em;">C</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>, followed by a line with <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mi>C</mi></msub></mrow>N_C</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 mathit mtight" style="margin-right:0.07153em;">C</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> coupon integers. Then the next line contains the number of products <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mi>P</mi></msub></mrow>N_P</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 mathit mtight" style="margin-right:0.13889em;">P</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>, followed by a line with <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mi>P</mi></msub></mrow>N_P</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 mathit mtight" style="margin-right:0.13889em;">P</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> product values. Here <span class="katex"><span class="katex-mathml"><math><mrow><mn>1</mn><mo>≤</mo><msub><mi>N</mi><mi>C</mi></msub><mo separator="true">,</mo><msub><mi>N</mi><mi>P</mi></msub><mo>≤</mo><mn>1</mn><msup><mn>0</mn><mn>5</mn></msup></mrow>1\le N_C, N_P \le 10^5</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:1.008548em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span><span class="mrel">≤</span><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 mathit mtight" style="margin-right:0.07153em;">C</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="mpunct">,</span><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 mathit mtight" style="margin-right:0.13889em;">P</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">1</span><span class="mord"><span class="mord mathrm">0</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">5</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 it is guaranteed that all the numbers will not exceed <span class="katex"><span class="katex-mathml"><math><mrow><msup><mn>2</mn><mrow><mn>3</mn><mn>0</mn></mrow></msup></mrow>2^{30}</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"><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 scriptstyle uncramped mtight"><span class="mord mathrm mtight">3</span><span class="mord mathrm mtight">0</span></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>.</p>
<h3 id="output-specification-">Output Specification:</h3>
<p>For each test case, simply print in a line the maximum amount of money you can get back.</p>
<h3 id="sample-input-">Sample Input:</h3>
<pre><code class="lang-in">4
1 2 4 -1
4
7 6 -2 -3
</code></pre>
<h3 id="sample-output-">Sample Output:</h3>
<pre><code class="lang-out">43
</code></pre>
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