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
MOD = 10 ** 9 + 7

N, K = map(int, input().split())

maxf = 2 * N + 10
f = [1 for _ in range(maxf)]
invf = [1 for _ in range(maxf)]

for i in range(1, maxf):
    f[i] = (i * f[i - 1]) % MOD

invf[maxf - 1] = pow(f[maxf - 1], MOD - 2, MOD)
for i in range(maxf - 1, 0, -1):
    invf[i - 1] = (i * invf[i]) % MOD


def comb(a, b):
    if b > a:
        return 0
    return (((f[a] * invf[b]) % MOD) * invf[a - b]) % MOD


A = sorted(list(map(int, input().split())))

res = 0
for i in range(N):
    res = (res + comb(i, K - 1) * (A[i] - A[N - i - 1])) % MOD

print(res)
