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
mod = 10 ** 9 + 7
N, K = map(int, input().split())
A = sorted(list(map(int, input().split())))
minus = 0
plus = 0
fact = [0] * (N+1)
fact[0] = 1
pow_fact = [0] * (N+1)
pow_fact[0] = 1
fa = 1
for i in range(1, N+1):
    fa *= i
    fa %= mod
    fact[i] = fa
    pow_fact[i] = pow(fa, mod-2, mod)
b = pow_fact[K-1]
for i in range(N-K+1):
    a = fact[N-i-1]
    c = pow_fact[N-i-K]
    comb = (a*b*c) % mod
    minus += (A[i] * comb) % mod
    plus += (A[-i-1] * comb) % mod
print((plus - minus) % mod)