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
import math
mod = 10**9+7
n,k = map(int,input().split())
b = math.factorial(k-1)%mod
fact = [0]*(n-k+1)
a = math.factorial(k-1)%mod
c = 1
for i in range(k-1, n):
    if i == k-1:
        fact[0] = (a*pow(b*c, mod-2, mod))%mod
    else:
        a = a*i%mod
        c = c*(i-k+1)%mod
        fact[i-k+1] = (a*pow(b*c, mod-2, mod))%mod
A = list(map(int,input().split()))
A.sort()
ans = 0
for i in range(k-1,n):
    ans += fact[i-k+1]*(A[i]-A[n-i-1])
    ans %= mod
print(ans)
