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 sys import stdin
#入力
readline=stdin.readline
N,K=map(int,readline().split())
A=list(map(int,readline().split()))
A.sort()

mod=10**9+7
fact=[1]*(N+1)
finv=[1]*(N+1)
inv=[1]*(N+1)
inv[0]=0
for i in range(2,N+1):
    fact[i]=(fact[i-1]*i%mod)
    inv[i]=(-inv[mod%i]*(mod//i))%mod
    finv[i]=(finv[i-1]*inv[i])%mod

def com(N,K,mod):
    if (K<0) or (N<K):
        return 0
    return fact[N]*finv[K]*finv[N-K]%mod

s=0
for i in range(N-1,K-2,-1):
    s+=A[i]*com(i,K-1,mod)
for i in range(N-K+1):
    s-=A[i]*com(N-i-1,K-1,mod)
s%=mod
print(s)