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())
l=sorted(list(map(int,input().split())))
mod=10**9+7
fact=[1]*(n+1)
inv=[1]*(n+1)
for i in range(2,n+1):
    fact[i]=i*fact[i-1]%mod
inv[-1]=pow(fact[-1],mod-2,mod)
for i in range(n,1,-1):
    inv[i-1]=inv[i]*i%mod
ans=0
for i in range(n):
    if i>=k-1:
        ans+=l[i]*fact[i]*inv[k-1]*inv[i-k+1]%mod
    if n-i-1>=k-1:
        ans-=l[i]*fact[n-i-1]*inv[k-1]*inv[n-i-1-k+1]%mod
    ans%=mod
print(ans)