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 = [int(i) for i in input().split()]
al = [int(i) for i in input().split()]
al.sort()
mod = 10 ** 9 + 7


kai = [1]
for i in range(1, n + 1):
    kai.append(kai[-1]*i%mod)




def comb(a, b, p=mod):
    if a < 0 or b < 0:
        return 0
    elif a < b:
        return 0
    c = 1
    c *= kai[a]
    c *= pow(kai[b], p - 2, p)
    c *= pow(kai[a - b], p - 2, p)
    return c % p


ans = 0
for i in range(k - 1, n):
    ans += al[i] * comb(i,k-1)
    ans %= mod
al = list(reversed(al))
for i in range(k - 1, n):
    ans -= al[i] * comb(i, k-1)
    ans %= mod
print(ans)
