Code Sequence

You want the next number in a sequence $S$ that a secret code generated. The code built the sequence by this procedure.

First, for each $k$ from 0 to 29, pick a number $C_k$ between 0 and 10006, inclusive.

Then, for each integer $n$ from 0 to $10^9$, inclusive:

• Write $n$ in binary.
• Take $C_k$ for every bit $k$ that is set in the binary representation of $n$. For example, when $n = 5$, bits 0 and 2 are set, so $C_0$ and $C_2$ are taken.
• Add the taken values together, divide by $10007$, and let the remainder be $S_n$.

You are given several consecutive values of $S$. You do not know where in the sequence your numbers begin, although you do know that at least one more number follows them, and you do not know which values of $C_k$ were chosen.

Find the next number in the sequence. If the input data cannot determine it, print UNKNOWN.

The first line contains an integer $T$, the number of test cases.

Each test case takes two lines.

• The first line contains an integer $N$, the number of elements of $S$ that you know.
• The second line contains the $N$ known elements, separated by single spaces. Each element is between 0 and 10006, inclusive.

Limits

• $1 \le T \le 20$
• $1 \le N \le 30$
• Each test case is a consecutive block of some sequence produced by the procedure above, and at least one more number follows that block.

For each test case, print one line containing "Case #$X$: $Y$", where $X$ is the test case number starting from 1 and $Y$ is the next number in the sequence. If the next number cannot be determined, write UNKNOWN in place of $Y$.

In the first sample case, $C_0$, $C_1$ and $C_2$ might have been 1, 2 and 4, with the given values starting at $n = 1$. If that is what happened, $C_3$ is unknown, so the next number could be anything, and the answer is UNKNOWN.

In the second sample case you cannot recover every value of $C_k$, and you cannot tell what $n$ is either. Even so, in any sequence produced this way, if 1, 10, 11, 200 occur in this order, the next value is always 201.