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
from math import factorial
n,k=map(int,input().split())
a=list(map(int,input().split()))
mod=10**9+7
ans=0
a.sort()
x=(factorial(n-1)*pow(factorial(k-1),mod-2,mod)*pow(factorial(n-k),mod-2,mod))%mod
y=1
for i in range(n-k+1):
  ans-=a[i]*x
  ans%=mod
  x=(x*(n-k-i)*pow(n-i-1,mod-2,mod))%mod
for i in range(k-1,n):
  ans+=a[i]*y
  ans%=mod
  y=(y*(i+1)*pow(i-k+2,mod-2,mod))%mod
print(ans)