| Matt Laundro is about to engage in his favourite activity — doing laundry! | |
| He's brought **L** indistinguishable loads of laundry to his local laundromat, | |
| which has **N** washing machines and **M** dryers. The **i**th washing machine | |
| takes **Wi** minutes to wash one load of laundry, and each dryer takes **D** | |
| minutes to dry a load of laundry. At any point in time, each machine may only | |
| be processing at most one load of laundry. | |
| As one might expect, Matt wants to wash and then dry each of his **L** loads | |
| of laundry. Each load of laundry will go through the following steps in order: | |
| 1. A non-negative amount of time after Matt arrives at the laundromat, Matt places the load in an unoccupied washing machine **i** | |
| 2. **Wi** minutes later, he removes the load from the washing machine, placing it in a temporary holding basket (which has unlimited space) | |
| 3. A non-negative amount of time later, he places the load in an unoccupied dryer | |
| 4. **D** minutes later, he removes the load from the dryer | |
| 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 **L** loads of laundry! | |
| ### Input | |
| Input begins with an integer **T**, 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 **L**, **N**, **M**, and **D** in that order. | |
| After that is a line containing **N** space-separated integers, the **i**th of | |
| which is **Wi**. | |
| ### Output | |
| For the **i**th trip, print a line containing "Case #**i**: " followed by the | |
| minimum time it will take Matt to finish his laundry. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 50 | |
| 1 ≤ **L** ≤ 1,000,000 | |
| 1 ≤ **N** ≤ 100,000 | |
| 1 ≤ **M** ≤ 1,000,000,000 | |
| 1 ≤ **D** ≤ 1,000,000,000 | |
| 1 ≤ **Wi** ≤ 1,000,000,000 | |
| ### Explanation of Sample | |
| 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. | |