Elevators in Jiayuan Students' Apartment

There are three elevators in the Building B of Jiayuan Students' Apartment in BJTU, which carry a lot of students to go up and down every day.
There're 16 floors in the Building B. The students living on the 1F don't need to wait for the elevators, so all the m students want to get to the 2F or higher.
Supposed that the capacity of each elevator is C( 1 ≤ C ≤ 13 ). Now there are m( 1 ≤ m ≤ 3*C ) students waiting for upstairs on the first floor, while all the three elevators stop on the first floor. You can arrange the way how they go upstairs, that Nobody will left on the first floor when the elevators are in the process of rising. How many times do the three elevators have to stop at least to carry all the m students to the right floor?

The first line of input contains a number t, which means there are t cases of the test data.
In each case of testing data, the first line contains two integers C and m.
In the next line, there are m integers f ( 2 ≤ f ≤ 16 ), indicate the floor a student wants to reach.

For each case of testing data, the first line is written as "Case n: X", where n is the case number, X is the minimum times the elevators have to stop in the process of rising.

2
1 3
2 4 16
2 6
9 9 9 6 6 6

Case 1: 3
Case 2: 4

madongfly & Louty (Special Thanks: mark.zhe)

2010 ACM-ICPC Multi-University Training Contest（14）——Host by BJTU