Problem Description

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

Yuta has an array $A$ of length $n$，for each $i(1 \leq i \leq n)$, $A[i]$ is integer and satisfies $1 \leq A[i] \leq m$. Rikka wants to add some **real** numbers in $[1,m]$ to the array in order to make the average number of $A$ less than or equal to the median number of $A$.

Now, Yuta wants to minimize the number of the added numbers, and on this basis, he wants to minimize the average number of $A$.

It is too difficult for Rikka. Can you help her?

Input

The first line contains a number $T(T \leq 1000)$——The number of the testcases. And there are no more than 5 testcases with $n>100$

For each testcase, the first line contains two numbers $n,m(1 \leq n \leq 10^5,1 \leq m \leq 10^9)$.

And the second line contains exactly $n$ numbers $A[i]$.

Output

For each testcase, print two numbers: the minimal number of the added numbers and the minimal average number of $A$. For the second number, You only need to reserve three decimal places.

1
3 5
1 2 5

1 3.000

You can insert a single number $4.000$.