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())
A = sorted(list(map(int, input().split())))
P = int(1e9+7)
ans = 0

kaizyo = [0]
kaizyo_inv = [0]
tmp = 1
for i in range(1, N+1):
    tmp = (tmp*i) % P
    kaizyo.append(tmp)
    kaizyo_inv.append(pow(tmp, P - 2, P))


def comb(n, r):
    if n < r or n == 0:
        return 0
    elif n == r or r == 0:
        return 1
    else:
        return kaizyo[n] * kaizyo_inv[r] * kaizyo_inv[n - r]


combs=[comb(i, K - 1)%P for i in range(N+1)]

for i, a in enumerate(A):
    ans = (ans + a * combs[i]) % P
    ans = (ans - a * combs[N - i - 1]) % P

print(ans)
