2016/round1/laundro_matt.html

<p>
Matt Laundro is about to engage in his favourite activity &mdash; doing laundry! He's brought <strong>L</strong> indistinguishable loads of laundry to his local laundromat, 
which has <strong>N</strong> washing machines and <strong>M</strong> dryers. The <strong>i</strong>th washing machine takes 
<strong>W<sub>i</sub></strong> minutes to wash one load of laundry, and each dryer takes <strong>D</strong> minutes to dry a load of laundry. 
At any point in time, each machine may only be processing at most one load of laundry.
</p>

<p>
As one might expect, Matt wants to wash and then dry each of his <strong>L</strong> loads of laundry. Each load of laundry will go through the following steps in order:
</p>

<p>
<ol>
<li>  A non-negative amount of time after Matt arrives at the laundromat, Matt places the load in an unoccupied washing machine <strong>i</strong> </li> 
<li>  <strong>W<sub>i</sub></strong> minutes later, he removes the load from the washing machine, placing it in a temporary holding basket (which has unlimited space) </li>
<li>  A non-negative amount of time later, he places the load in an unoccupied dryer </li>
<li>  <strong>D</strong> minutes later, he removes the load from the dryer </li>
</ol>
</p>

<p>
Matt can instantaneously add laundry to or remove laundry from a machine. 
Help Matt minimize the amount of time (in minutes after he arrives at the laundromat) after which he can be done drying all <strong>L</strong> loads of laundry!
</p>


<h3>Input</h3>
<p>
Input begins with an integer <strong>T</strong>, the number of times Matt goes to the laundromat.
For each trip to the laundromat, there is first a line containing the space-separated integers 
<strong>L</strong>, <strong>N</strong>, <strong>M</strong>, and <strong>D</strong> in that order.
After that is a line containing <strong>N</strong>
space-separated integers, the <strong>i</strong>th of which is <strong>W<sub>i</sub></strong>.
</p>


<h3>Output</h3>
<p>
For the <strong>i</strong>th trip, print a line containing "Case #<strong>i</strong>: " followed by
the minimum time it will take Matt to finish his laundry.
</p>


<h3>Constraints</h3>
<p>
1 &le; <strong>T</strong> &le; 50 <br />
1 &le; <strong>L</strong> &le; 1,000,000 <br />
1 &le; <strong>N</strong> &le; 100,000 <br />
1 &le; <strong>M</strong> &le; 1,000,000,000 <br />
1 &le; <strong>D</strong> &le; 1,000,000,000 <br />
1 &le; <strong>W<sub>i</sub></strong> &le; 1,000,000,000 <br />
</p>


<h3>Explanation of Sample</h3>
<p>
In the first case, Matt has just one load of laundry. He washes it for 1200 minutes, and dries it for 34 minutes.
In the second case, Matt uses the 1-minute washer for both loads of laundry. The second load finishes at the 2-minute mark, so it finishes drying at the 12-minute mark.
</p>