Migrated from Lutece 85 Counting Pair

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Description

Bob hosts a party and invites $N$ boys and $M$ girls. He gives every boy here a unique number $N_i$($1 \leq N_i \leq N$). And for the girl, everyone holds a unique number $M_i$($1 \leq M_i \leq M$), too.

Now when Bob name a number $X$, if a boy and a girl wants and their numbers' sum equals to $X$, they can get in pair and dance.

At this night, Bob will name $Q$ numbers, and wants to know the maxinum pairs could dance in each time. Can you help him?

Input

First line of the input is a single integer $T$($1 \leq T \leq 30$), indicating there are $T$ test cases.

The first line of each test case contains two numbers $N$ and $M$($1 \leq N,M \leq 100000$).

The second line contains a single number $Q$($1 \leq Q \leq 100000$).

Each of the next $Q$ lines contains one number $X$($0 \leq X \leq 10^9$), indicating the number Bob names.

Output

For each test case, print Case #t: first, in which t is the number of the test case starting from $1$.

Then for each number Bob names, output a single num in each line, which shows the maxinum pairs that could dance together.

Samples

1
4 5
3
1
2
3

Case #1:
0
1
2

Note

This problem has very large input data. scanf and printf are recommended for C++ I/O.

Resources

Sichuan State Programming Contest 2012