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
To output my sequence of pseudorandom 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 S 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 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.
1 ≤ T ≤ 100.
1 ≤ K ≤ 10.
The K integers will be consecutive elements of
a sequence generated by a random number generator of
the type described above.
1 ≤ D ≤ 4.
1 ≤ D ≤ 6.
Input 
Output 
3

Case #1: 10
