2016/round3/matt_laundro.md

Matt Laundro is about to engage in his favourite activity — doing laundry!
He's brought **L** loads of laundry to his local laundromat, which has
recently been cracking down on excessive washer and dryer usage. It turns out
the other customers weren't very thrilled when they saw Matt using a billion
washers and dryers simultaneously, so he's now been restricted to just one
washer and one dryer. Matt's **i**th load of laundry takes **Wi** minutes to
wash, and **Di** minutes to dry. As is usually the case with laundry, each
load takes at least as long to dry as it does to wash. 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. Unfortunately, the laundromat closes in **K** minutes, so he might
not be able to get through every load. But he'll try his best! If he chooses
to wash and dry the **i**th load of laundry, it 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 the washing machine 
  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 the dryer 
  4. **Di** minutes later, he removes the load from the dryer 

Matt can instantaneously add laundry to or remove laundry from a machine. He
can choose to wash and dry any of his loads and they can be washed and dried
in any order as long as they each follow the steps above. Help Matt maximize
the number of loads he can finish washing and drying in **K** minutes, and
amongst all the ways he could finish that many loads, find the minimum amount
of time it will take for all of those loads to be washed and dried.

### Input

In this problem, the sequences **W** and **D** are generated using a pseudo-
random number generator. The generator first produces two length-**L**
sequences **X** and **Y**. **X1** and **Y1** are given, and the remaining
terms **X2**...**XL** and **Y2**...**YL** are computed as follows:

**Xi** = ( (**Ax** * **Xi-1** \+ **Bx**) mod **Cx**) + 1   
**Yi** = ( (**Ay** * **Yi-1** \+ **By**) mod **Cy**) + 1 

After **X** and **Y** are generated, **W** and **D** are computed as follows:

**Wi** = min {**Xi**, **Yi**}   
**Di** = max {**Xi**, **Yi**} 

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** and **K**, then a line containing the
space-separated integers **Ax**, **Bx**, **Cx**, and **X1**, then a line
containing the space-separated integers **Ay**, **By**, **Cy**, and **Y1**.

### Output

For the **i**th trip, print a line containing "Case #**i**: " followed by the
maximum number of loads Matt can finish before the laundromat closes, and the
minimum amount of time it will take to finish that many.

### Constraints

1 ≤ **T** ≤ 50  
1 ≤ **L** ≤ 500,000  
1 ≤ **K** ≤ 1,000,000,000  
1 ≤ **Ax**, **Bx**, **Cx** ≤ 1,000,000,000  
1 ≤ **Ay**, **By**, **Cy** ≤ 1,000,000,000  
1 ≤ **X1** ≤ **Cx**  
1 ≤ **Y1** ≤ **Cy**  

### Explanation of Sample

In the first case, **W** and **D** are the same: {1, 3, 5, 7}. Matt can finish
the first three loads in 14 minutes. He starts by washing the third load,
which takes 5 minutes. Then, while that load is drying he can wash the first
and second loads. The second case is the same, except Matt now has just enough
time to wash all of the loads. He can start by washing the fourth load, which
takes 7 minutes. In the third case, **W** = {2, 1, 6, 2, 1, 3} and **D** = {3,
4, 7, 5, 10, 6}.