Problem

You own a factory with two assembly lines. The first assembly line makes boxes, and the second assembly line makes toys to put in those boxes. Each type of box goes with one type of toy and vice-versa.

At the beginning, you pick up a box from the first assembly line and a toy from the second assembly line. You then have a few options.

Warning: The two assembly lines make a lot of boxes and toys. However, they tend to make one kind of thing for a long period of time before switching.

Input

The first line of the input gives the number of test cases, T. T test cases follow.

Each test case begins with a line contains two integers N and M. It is followed by a line containing 2 N integers a₁, A₁, a₂, A₂, ..., a_N, A_N, and another line containing 2 M integers b₁, B₁, b₂, B₂, ..., b_M, B_M.

This means that the first assembly line will make a₁ boxes of type A₁, then a₂ boxes of type A₂, etc., until it finishes with a_N boxes of type A_N. Similarly, the second assembly will make b₁ toys of type B₁, followed by b₂ toys of type B₂, etc., until it finishes with b_M toys of type B_M.

A toy can be matched with a box if and only if they have the same type number.

Output

For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1), and y is the largest number of boxed toys that you can send out to customers.

Limits

Memory limit: 1GB.

Time limit: 30 6 seconds per test set.

1 ≤ T ≤ 100.

1 ≤ a_i, b_i ≤ 10¹⁶.

1 ≤ A_i, B_i ≤ 100.

Test set 1 (Visible Verdict; 12 Points)

1 ≤ N ≤ 3.

1 ≤ M ≤ 100.

Test set 2 (Hidden Verdict; 23 Points)

1 ≤ N, M ≤ 100.

Sample

4
3 3
10 1 20 2 25 3
10 2 30 3 20 1
3 5
10 1 6 2 10 1
5 1 3 2 10 1 3 2 5 1
3 5
10 1 6 2 10 1
5 1 6 2 10 1 6 2 5 1
1 1
5000000 10
5000000 100

Case #1: 35
Case #2: 20
Case #3: 21
Case #4: 0