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
$1<=T<=100$
$1<=N<=50000$
$1<=S<=1000000000$
$1<=Arr_i<=10000$