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

mod = 10**9+7

fact = [1]
for i in range(n):
    fact.append(fact[-1]*(i+1)%mod)

finv = [1]*(n+1)
finv[n] = pow(fact[-1],mod-2,mod)
for i in range(n-1,0,-1):
    finv[i] = ((i+1)*finv[i+1])%mod

def combi(n,k,mod):
    return (fact[n]*finv[k]*finv[n-k])%mod

l.sort()

ans = 0
for i in range(n-k+1):
    tmp = combi(n-i-1,k-1,mod)
    ans += tmp*(l[-i-1]-l[i])
    ans %= mod

print(ans%mod)






