For a finite set of integers X, let f(X)=\max X - \min X.

Given are N integers A_1,...,A_N.

We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.

Since the answer can be enormous, print it \bmod (10^9+7).

Constraints

* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:


N K
A_1 ... A_N


Output

Print the answer \bmod (10^9+7).

Examples

Input

4 2
1 1 3 4


Output

11


Input

6 3
10 10 10 -10 -10 -10


Output

360


Input

3 1
1 1 1


Output

0


Input

10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0


Output

999998537
import sys

read = sys.stdin.buffer.read
input = sys.stdin.buffer.readline
inputs = sys.stdin.buffer.readlines


mod=10**9+7
# rstrip().decode('utf-8')
# map(int,input().split())
#import numpy as np


def main():
	n,k=map(int,input().split())
	A=list(map(int,input().split()))
	A.sort()
	
	comb=[1]
	for i in range(n-k):
		comb.append((comb[-1]*(k+i)*pow(i+1,mod-2,mod))%mod)
	ans=0
	
	for i in range(n-k+1):
		ans+=((comb[i]*A[k-1+i])-(comb[i]*A[n-k-i]))%mod
		ans=ans%mod
	print(ans)


if __name__ == "__main__":
	main()
