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
mod = 10**9+7
N,K = map(int,input().split())
fact = [1]*(N+1)
for i in range(N):
    fact[i+1] = (i+1)*fact[i]
    fact[i+1] %= mod
factinv = [1]*(N+1)
for i in range(N+1):
    factinv[i] = pow(fact[i],mod-2,mod)

def comb(n,k):
    return fact[n]*factinv[k]*factinv[n-k]%mod

A = list(map(int,input().split()))
A.sort()
M = 0
m = 0
for n in range(K-1,N):
    M += A[n]*comb(n,K-1)
    M %= mod
for n in range(N-K+1):
    m += A[n]*comb(N-n-1,K-1)
    m %= mod
print((M-m)%mod)