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=sorted([int(i) for i in input().split()])
B=[A[-i-1] for i in range(N)]
mod=10**9+7
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1;Finv[0]=1
def inv(x):
    return pow(x,mod-2,mod)
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%mod
    Finv[i+1]=inv(Fact[i+1])
def C(n,k):
    return (Fact[n]*((Finv[k]*Finv[n-k])%mod))%mod
ans1=0
ans2=0
for i in range(K-1,N):
    #print(C(i,K-1))
    ans1+=A[i]*C(i,K-1)
    ans1%=mod
    ans2+=B[i]*C(i,K-1)
    ans2%=mod

print((ans1-ans2)%mod)
