You will be given two integers N and K$,$ in addition to an array Arr of size N$.$

You can calculate the function F$($Arr$)$ as follows:

$|$Arr i $-$ Arr i$+$k$|$ from i $=0$ to n$-$k

You are allowed to rearrange the elements of Arr any way you want.

Find the minimum possible value of F$($Arr$).$ Since the answer can be very large return i modulo $10^9+7.$

Notes:

$$ It is given that Arr follows $1$ basedindexing.

Input Format

The first line contains an integer, N$,$ denoting the number of elements in Arr.

The next line contains an integer, k$,$ denoting the value of k to use in calcuang F$($Arr$)$

Each line i of the N subsequent lines $($where i N$)$ contains an integer descring A

Constraints

N

$1=$K$=$min$$N$-1,4*10^3$

$-10^9$Arr$[$i$=10^9$You will be given two integers $N$ and $K,$ in addition to an array Arr of size $N$

You can calculate the function Arr