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
from itertools import accumulate

mod = 10 ** 9 + 7

N, K = map(int, input().split())
A = sorted([int(x) for x in input().split()])

f = [1 for _ in range(N + 1)]
inv = [1 for _ in range(N + 1)]
finv = [1 for _ in range(N + 1)]

for i in range(2, N + 1):
    f[i] = f[i - 1] * i % mod
    inv[i] = mod - inv[mod % i] * (mod // i) % mod
    finv[i] = finv[i - 1] * inv[i] % mod
comb = [f[n] * (finv[K - 1] * finv[n - (K - 1)] % mod) % mod for n in range(K - 1, N)]

ans = 0
for i in range(N - K + 1):
    ans += comb[i] * (A[i + K - 1] - A[N - i - K])
    ans %= mod
print(ans)
