De-RNG-ed (Small)

I want to build an online poker site. One important part of such a system is the random number generator. It has to be fast and random enough. Here is the compromise I came up with.

I need to generate random numbers of length at most $D$. First I pick a prime $P$ with $P \le 10^D$. Then I pick non-negative integers $A$ and $B$. Finally I pick an integer seed $S$ with $0 \le S \le P-1$.

To print my sequence of pseudo-random numbers I first print $S$, then update $S$ with

$S := (A \times S + B) \bmod P$

I print the updated $S$ as the next term of the sequence and update it again with the same formula. I repeat that as often as I want.

Do you think this is a good random number generator? Write a program that reads $K$ consecutive terms of a sequence produced this way and prints the term that comes next.

The first line contains the number of test cases $T$. The first line of each test case contains $D$ and $K$. The next line contains $K$ consecutive terms produced by a random number generator of the kind described above.

Limits

• $1 \le T \le 100$
• $1 \le D \le 4$
• $1 \le K \le 10$
• The $K$ given integers are consecutive terms of a sequence produced by a generator of the kind described above.

For each test case print one line in the form Case #x: y, where $x$ is the test case number starting from 1.

Consider every choice of a prime $P \le 10^D$ and non-negative integers $A$ and $B$ that produces the $K$ given terms. If all of those choices give the same next term, then $y$ is that value. If two or more different next terms are possible, then $y$ is I don't know.