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 = [int(x) for x in input().split()]
A.sort()
res = 0
MOD = 10**9+7
nCk_2 = dict()
fac, finv, inv = [0]*(N+1), [0]*(N+1), [0]*(N+1)
fac[0] = fac[1] = 1
finv[0] = finv[1] = 1
inv[1] = 1
for i in range(2,N+1):
    fac[i] = fac[i-1]*i%MOD
    inv[i] = MOD-inv[MOD%i]*(MOD//i)%MOD
    finv[i] = finv[i-1]*inv[i]%MOD
def comb(n, k):
    return (fac[n]*((finv[k]*finv[n-k])%MOD))%MOD
s = [1,-1]
for m in range(2):
    for i in range(K-1,N):
        res = (res + s[m]*int((A[i])*comb(i,K-1)))%MOD
    A = sorted(A, reverse=True)
print(res)
