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())
p = 10**9+7
f=[1]
for i in range(1,N+1):
  f.append(f[-1]*i % p)

def nCk(n,k):
  return f[n]*pow(f[n-k], p-2, p)*pow(f[k], p-2, p)

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

ans = 0
for i in range(N-K+1):
  ans -= (a[i] * nCk(N-i-1, K-1)) % p
  ans += (a[N-i-1] * nCk(N-i-1, K-1)) % p
print(ans % p)