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=list(map(int,input().split()))
a.sort()
a.reverse()
mod=10**9+7
fact = [1]*100005
inv = [1]*100005
for i in range(2,100003):
	fact[i] = (fact[i-1]*i)%mod
for i in range(1,100003):
	inv[i] = pow(fact[i],mod-2,mod)

#n!//k!(n-k)!
def nCk(n,k):
	return fact[n]*inv[k]%mod*inv[n-k]%mod

ans = 0

for i in range(n-k+1):
	ans += (a[i]-a[n-1-i])*nCk(n-1-i,k-1)
	ans%=mod
print(ans)