| It's time to clean up your friends list after friending too many people on | |
| Facebook over the winter. The set of your friends' user ids is **F** = | |
| {**x0**, **x1**, ..., **xn-1**}. Each friend from **F** is on zero or more | |
| friend lists that you use to organize your friends. There are **M** friend | |
| lists, **c0**, **c1**, ..., **cm-1**. You can unfriend (remove from **F**) | |
| some of your friends, but because you want to stay in touch with people, you | |
| can only unfriend one person from each friend list. You may also choose not to | |
| unfriend anyone from friend list. Any friend that isn't on a friend list | |
| cannot be unfriended. | |
| Your goal is to find the maximum possible distance between the two friends | |
| whose user ids are the closest after you are done unfriending people. The | |
| distance between user id **x** and user id **y** is defined as | |
| abs(**x**-**y**). | |
| ### Input | |
| The first line contains a positive integer **T**, the number of test cases. | |
| **T** test cases follow. | |
| The first line of each test case contains the number of friends **N**, and | |
| number of friend lists **M**, separated by a space. The second line contains | |
| **x0** and integer parameters **a**, **b**, and **p**, separated by spaces. | |
| You must use these to generate the remaining numbers **x1**, …, **xn-1** | |
| according to this formula: | |
| > **xi** = (**xi-1** * **a** \+ **b**) mod **p** | |
| The next M lines of each test case define the friend lists for that test case. | |
| Each line consists of the following integers, separated by spaces: **size**, | |
| **y0**, **a**, **b**. The **size** is the number of friends in the friend | |
| list. **y0** is the index in F of the first friend in the list. You must | |
| generate the remaining friends in the friend list **y1**, …, **yn-1** | |
| according to the following formula: | |
| > **yi** = (**yi-1** * **a** \+ **b**) mod **n** | |
| If a friend list contains more than one of a given index, consider it to only | |
| contain that index once. | |
| ## Constraints | |
| 1 ≤ **T** ≤ 20 | |
| 2 ≤ **n** ≤ 50 000 | |
| 0 ≤ **m** ≤ 1 500 | |
| 0 ≤ sum of sizes of all friend lists ≤ 1 000 000 | |
| **Numbers used in generators:** | |
| 0 < **a**, **p** < 230 | |
| 0 ≤ **b** < 230 | |
| ### Output | |
| For each of the test cases numbered in order from **1** to **T**, output "Case | |
| #", followed by the case number, followed by ": ", followed by the maximum | |
| possible distance between the two closest user ids that you are still friends | |
| with for that case. | |