#213522. [GCJ 2010 #3] De-RNG-ed

I want to make an online poker website. A very important component of such a system is the random number generator. It needs to be fast and random enough. Here is a compromise I came up with. I need a way to generate random numbers of length at most . My plan is to select a prime number . I am also going to pick non-negative integers and . Finally, I'm going to pick an integer seed between and , inclusive.

To output my sequence of pseudo-random numbers, I'm going to first output and then compute the new value of like this:

Then I will output the new value of as the next number in the sequence and update again by using the same formula. I can repeat this as many times as I want.

Do you think that this is a good random number generator? Can you write a program that takes consecutive elements of a sequence that was generated by my random number generator, and prints the next element of the sequence?

The first line of the input gives the number of test cases, . test cases follow. Each one starts with a line containing and . The next line contains consecutive elements generated by a random number generator of the kind described above.

For each test case, output one line containing "Case #: ", where is the case number (starting from 1) and is either the next number in the sequence, or the string "I don't know." if the answer is ambiguous.

样例输入 1

3
2 10
0 1 2 3 4 5 6 7 8 9
3 1
13
1 5
6 6 6 6 6

样例输出 1

Case #1: 10
Case #2: I don't know.
Case #3: 6

Limits

• .
• .
• The integers will be consecutive elements of a sequence generated by a random number generator of the type described above.

Small dataset (4 Pts, Test set 1 - Visible)

• .

Large dataset (10 Pts, Test set 2 - Hidden)

• .