JLNT  Jarin Loves New Task
Jarin has got a new task. She has to connect towers by wire.
Given
 Number of towers N (2<=N<=1000)
 The length of wire L (0<=L<=5000).
 Coordinates of each tower in 1D starting from left to right and each coordinate will be a positive distinct integer (0<=a[i]<=5000).
Her task is to maximize the number of connected towers using that wire. But she has to make sure each tower is either connected with its left tower or its right tower or have no connection. She has to cut off the wire into particular sizes she wants to use.
It so difficult task for her. So you must have to help her :) .
Input
Input starts with an integer T (≤ 100), denoting the number of test cases.
Each case starts with two integers N and L . Next line contains N space separated integers.
Output
For each case, print the case number and expected answer.
Sample Input 
Output for Sample Input 
1 6 2 1 2 3 4 5 6 
Case 1: 4 
Problem Setter: Ajharul Islam Barid
Special Thanks: Abu Zafar Newton.
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Jacob Plachta:
20141015 08:32:01
To clarify, not all of the wire must be used, and a tower cannot be connected both on its left and on its right. Last edit: 20141015 08:34:55 

Ajharul Islam Barid:
20141014 10:25:23
Coordinates strictly positive.


Ajharul Islam Barid:
20141014 10:25:23
6 1


Jacob Plachta:
20141014 10:25:23
Coordinates are nonnegative, not strictly positive. Also, can you check that the data's fine? 
Added by:  Ajharul Islam Barid 
Date:  20140924 
Time limit:  0.5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 