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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 D. My plan is to select a prime number P ≤ 10D. I am also going to pick non-negative integers A and B. Finally, I'm going to pick an integer seed S between 0 and P-1, inclusive.
To output my sequence of pseudo-random numbers, I'm going to first output S and then compute the new value of S like this:
S := (A*S + B) mod P.
Then I will output the new value of S as the next number in the sequence and update Sagain 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 K 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, T. T test cases follow. Each one starts with a line containing D and K. The next line contains K consecutive elements generated by a random number generator of the kind described above.
For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is either the next number in the sequence, or the string "I don't know." if the answer is ambiguous.
3 2 10 0 1 2 3 4 5 6 7 8 9 3 1 13 1 5 6 6 6 6 6
Case #1: 10 Case #2: I don't know. Case #3: 6