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_=10**5+3
mod=10**9+7
fac=[1]*(n_+1)
for i in range(1,n_+1):
    fac[i]=fac[i-1]*i%mod
inv =[1]*(n_+1)
inv[n_]=pow(fac[n_],mod-2,mod)
for i in range(n_-1,0,-1):
    inv[i]=inv[i+1]*(i+1)%mod
def nCr(n,r):
    if n<=0 or r<0 or r>n:
        return 0
    return fac[n]*inv[r]%mod*inv[n-r]%mod

n,k=map(int,input().split())
A=list(map(int,input().split()))
A.sort()
ans=0
for i in range(n-k+1):
    ans=(ans+(A[n-i-1]-A[i])*nCr(n-i-1,k-1))%mod
print(ans)