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
input = sys.stdin.readline
sys.setrecursionlimit(10**5)

from bisect import bisect_left, bisect_right

N, K = map(int, input().split())
A = [int(i) for i in input().split()]
mod = 10 ** 9 + 7

A.sort()

fac = [1]
inv = [1]
for i in range(1, N + 1) :
  fac.append(fac[-1] * i % mod)
  inv.append(pow(fac[-1], mod - 2, mod))
  
def nCr(n, r) :
  if r < 0 or n < r :
    return 0
    
  return fac[n] * inv[n - r] * inv[r] % mod

ret = 0
for i in range(N) :
  l = N - i - 1
  u = i
  ret += A[i] * (nCr(u, K - 1) - nCr(l, K - 1))
  ret %= mod
  
print(ret)