You are given an array \(Arr_i\) of size N. You have to find the maximum value of K such that after choosing K numbers from the array the \(DiffValue\) of chosen numbers is less than or equal to S.
\(DiffValue\) for a set of integers is defined as the largest possible difference among any two integers of the set. However if you choose K numbers from the array, value of all the chosen numbers get multiplied by K.
Hence print two integers i.e the largest value of number K and largest possible \(DiffValue\) corresponding to value of K.
Input Format
First line contains T i.e number of testcases.
For each testcase,
First line contains two space separated integers denoting N and S and
The next line contains N space separated integers denoting the array.
Output Format
Print answer to each testcase in separate line.
For each testcase print two space separated integers denoting the value of K and \(DiffValue\).
Constraints
\(1<=T<=100\)
\(1<=N<=50000\)
\(1<=S<=1000000000\)
\(1<=Arr_i<=10000\)
For testcase 1 if we choose k=2 numbers i.e {1,2}. So the numbers get transformed into {1x2,2x2} = {2,4} giving the DiffValue=2 which is <= 3. Hence answer is 2 2.
