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
# coding=utf-8

get = lambda: int(raw_input().strip())
gets = lambda: map(int, raw_input().strip().split())
getss = lambda x: [gets() for _ in xrange(x)]

n, k = gets()
A = sorted(gets())
res = 0

mod = 10**9 + 7


def inv(a):
    return pow(a, mod - 2, mod)


def power(x, y, m):
    if (y == 0):
        return 1
    p = power(x, y // 2, m) % m
    p = (p * p) % m
    if(y % 2 == 0):
        return p
    else:
        return ((x * p) % m)


def C(n, k):
    res = 1
    for i in xrange(1, k + 1):
        res *= n - i + 1
    for i in xrange(1, k + 1):
        res /= i
    return res

res = 0
combi = 1
for i in xrange(k - 1, n):
    # combi2 = C(i, k - 1)
    if i >= k:
        combi = combi * i % mod
        combi = combi * inv(i + 1 - k) % mod
    # print i, combi, combi2
    res += (A[i] - A[~i]) * combi % mod
print res % mod
