| Pierre Peintre is slaving away over a new abstract painting entitled _Rain | |
| Over New York_. This will be a simple yet powerful piece, omitting incidental | |
| details such as busy city dwellers shielding themselves with umbrellas, and | |
| instead focusing on the fundamental atmosphere of a rainy metropolitan day. It | |
| will be painted on a canvas which is subdivided into a grid of 1cm x 1cm | |
| cells, with **N** rows and **M** columns. Each cell in this grid will be | |
| filled in with a solid color, either black, white, grey, or blue. | |
| The lower portion of _Rain Over New York_ will depict the skyline of New York | |
| City. In each column _i_, the bottom-most **Hi** cells will be painted grey to | |
| represent an austere skyscraper. | |
| Somewhere above the buildings, Pierre will place a single, innocent raincloud. | |
| In particular, the cloud can be any rectangle of white cells on the canvas, as | |
| long as none of them are supposed to be grey. | |
| Below the cloud, there must be a gentle rainfall, of course. Every cell which | |
| has a white cell somewhere directly above it and a grey cell somewhere | |
| directly below it, and which isn't supposed to be white or grey itself, should | |
| be painted blue. Note that there may be no such cells, if the cloud is | |
| immediately above the skyline. | |
| All of the remaining cells in the painting will be painted black, providing a | |
| serene nighttime backdrop for the scene. | |
| Pierre knows that every painting he can produce like this will sell for an | |
| enormous sum of money, but only if it's unique. As such, he'll paint as many | |
| different paintings as he can by varying the position and dimensions of the | |
| raincloud depicted in them. Two paintings are considered distinct if at least | |
| one cell on the canvas is a different color in one painting than it is in the | |
| other. | |
| As an example, below is an illustration of 1 of the 246 possible paintings for | |
| the fourth sample case: | |
|  | |
| Thanks to the incredible sum of money which Pierre is sure to make from these | |
| works, he'll be able to purchase all of the paint that he'll need. He always | |
| buys his paint in cans of a fixed size, each of which contains just enough to | |
| cover a surface of 1,000,000,007 cm2, and for each color, he'll buy just | |
| enough such cans in order to be able to complete all possible distinct | |
| variations of his painting, once each. Always one to plan ahead, Pierre would | |
| like to figure out exactly how much paint of each color he'll have left over | |
| when he's done. | |
| The sequence **H1..M** can be constructed by concatenating **K** temporary | |
| sequences of values **S1..K**, the _i_th of which has a length of **Li**. It's | |
| guaranteed that the sum of these sequences' lengths is equal to **M**. For | |
| each sequence **Si**, you're given **Si,1**, and **Si,2..Li** may then be | |
| calculated as follows, using given constants **Ai** and **Bi**: | |
| **Si,j** = ((**Ai** * **Si,j-1** \+ **Bi**) % (**N** \- 1)) + 1 | |
| ### Input | |
| Input begins with an integer **T**, the number of different base skylines | |
| Pierre wants to use. For each skyline, there is first a line containing the | |
| three space-separated integers, **N**, **M**, and **K**. Then **K** lines | |
| follow, the _i_th of which contains the four space-separated integers **Li**, | |
| **Si,1**, **Ai**, and **Bi**. | |
| ### Output | |
| For the _i_th skyline, print a line containing "Case #**i**: " followed by | |
| four space-separated integers, the total amount of black, white, grey, and | |
| blue paint which Pierre will have left over, respectively (in cm2), after | |
| completing all possible variations of his painting. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 100 | |
| 2 ≤ **N** ≤ 1,000,000,000 | |
| 1 ≤ **M** ≤ 200,000 | |
| 1 ≤ **K** ≤ 100 | |
| 1 ≤ **Li** ≤ M | |
| 1 ≤ **Hi**, **Si,j** ≤ **N** \- 1 | |
| 0 ≤ **Ai**, **Bi** < **N** \- 1 | |
| ### Explanation of Sample | |
| In the first case, there's only one possible painting, with the top cell | |
| painted white, and the remaining two cells painted grey. Pierre will buy 1 can | |
| each of white and grey paint, and have 1,000,000,006 and 1,000,000,005 cm2 | |
| left over of those colors, respectively. | |
| In the second case, there are 6 possible paintings: three with the cloud | |
| covering one cell, two with the cloud covering two cells, and one with the | |
| cloud covering three cells. Therefore, Pierre will use 10 cm2 of white paint | |
| in total. | |
| The fourth case corresponds to the picture shown above. | |