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(map(int,input().split()))

def cmb(n,r,mod):
    if (r<0 or r>n):
        return 0
    r=min(r,n-r)
    return g1[n]*g2[r]*g2[n-r]%mod

mod=10**9+7
N=10**5
g1=[1,1]
g2=[1,1]
inverse=[0,1]

for i in range(2,N+1):
    g1.append((g1[-1]*i)%mod)
    inverse.append((-inverse[mod%i]*(mod//i))%mod)
    g2.append((g2[-1]*inverse[-1])%mod)

ans=0
for i in range(n-k+1):
    ans+=cmb(n-1-i,k-1,10**9+7)*(A[-i-1]-A[i])%(10**9+7)
    ans%=10**9+7
print(ans)