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 sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N, K = mapint()
As = list(mapint())
mod = 10**9+7
As.sort()

pos = {}
neg = {}
pos[0] = 1
neg[0] = 1
for i in range(1, 10**5+3):
    pos[i] = (pos[i-1]*i)%mod
    neg[i] = pow(pos[i], mod-2, mod)

mini = 0
maxi = 0
for i, a in enumerate(As):
    if i<=N-K:
        mini += a*pos[(N-i-1)]*neg[K-1]*neg[N-i-K]
        mini %= mod
    if i>=K-1:
        maxi += a*pos[i]*neg[K-1]*neg[i-K+1]
        maxi %= mod
print((maxi-mini)%mod)