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
n,k=map(int,input().split())
A=list(map(int,input().split()))
MOD=10**9+7
ans=0

L=[1]*(n+1)
Linv=[1]*(n+1)
inv=[0]+[1]*n

for i in range(2,n+1):
    L[i]=(L[i-1]*i)%MOD
    inv[i]=(MOD-inv[MOD%i]*(MOD//i))%MOD
    Linv[i]=(Linv[i-1]*inv[i])%MOD

def cmb(n,k):
    return (((L[n]*Linv[k])%MOD)*Linv[n-k])%MOD

A.sort()

for j in range(n-k+1):
    ans+=((A[-1-j]-A[j])*cmb(n-1-j,k-1))%MOD

if ans>=0:
    print(ans%MOD)
else:
    print(MOD+ans)
