Migrated from Lutece 1471 Alice and Bob are playing number

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Description

Bob and his girl friend are playing game together. This game is like this:

There are $n$ numbers.

If op = $1$, Bob wants to find two numbers $a_i$ and $a_j$, that $a_i$ & $a_j$ will become maximum value.

If op = $2$, Bob wants to find two numbers $a_i$ and $a_j$ ,that $a_i$ ^ $a_j$ will become maximum value.

If op = $3$, Bob wants to find two numbers $a_i$ and $a_j$, that $a_i$ | $a_j$ will become maximum value.

Notice:

& for bitwise AND. (4 & 2) is 0, (4 & 5) is 4.

^ for bitwise XOR. (4 ^ 2) is 6, (4 ^ 5) is 1.

| for bitwise OR. (4 | 2) is 6, (4 | 5) is 5.

Input

First line is a positive integer $T$ , represents there are $T$ test cases.

For each test case:

First line includes two numbers $n (2 \leq n \leq 100000)，op( 1\leq op \leq 3)$.

The next line contains $n$ numbers: $a_1, a_2 ,… , a_n (1\leq a_i \leq 1000000)$.

Output

For the $i$-th test case, first output Case #i: in a single line.

Then output the answer of $i$-th test case.

Samples

3
2 1
4 2
2 2
4 2
2 3
4 2

Case #1: 0
Case #2: 6
Case #3: 6

Resources

“玲珑杯”ACM比赛 Round #2