A + B Problem

Do you know the famous Fibonacci sequence? It is defined by the recurrence
F₀ = 0, F₁ = 1 and F_n = F_n-1 + F_n-2 for n ≥ 2.
The Fibonacci numbers have many interesting properties. One of them is that the Fibonacci numbers can be used to represent integers. Every positive integer has a unique representation of the form
n = F_k1 + F_k2 + … + F_km, k_i ≥ k_i-1 + 2 for 2 ≤ i ≤ m and k₁ ≥ 2
For example, 6 can be represented as F₂+F₅ and 12 can be represented as F₂+F₄+F₆.
Now you know how to represent positive integers with the Fibonacci numbers, can you add them? Given two Fibonacci formed integers, you should calculate the sum of them.

The first line contains a single integer T, indicating the number of test cases.
Each test case contains two lines; each line contains a single integer m followed by m integers k₁, k₂, …, k_m indicate a Fibonacci formed integer F_k1+F_k2+…+F_km.
The input will be always correct.

Technical Specification

1. 1 <= T <= 100
2. 1 <= m <= 100
3. 2 <= k_i <= 1000000

For each test case, output the case number first, then a single line indicates the sum of the two Fibonacci formed integer. The sum should be Fibonacci formed like the input.

2
1 2
2 2 4
3 2 4 6
2 2 5

Case 1:
1 5
Case 2:
2 5 7

Dumbear@WHU

The 6th Central China Invitational Programming Contest and 9th Wuhan University Programming Contest Final