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(i) for i in input().split()]
a.sort()
mod = 10**9+7
fac = [0]*(n+1)
finv = [0]*(n+1)
def comb(n,k):
    if n < k: return 0
    if n < 0 or k < 0: return 0
    return fac[n]*finv[k]%mod*finv[n-k]%mod
fac[0] = finv[0] = 1
for i in range(1,n+1):
    fac[i] = fac[i-1]*i%mod
    finv[i] = pow(fac[i],mod-2,mod)
smin = 0
smax = 0
for i in range(n):
    smin += (a[i]*comb(n-i-1,k-1))%mod
    smin %= mod
    smax += (a[n-1-i]*comb(n-i-1,k-1))%mod
    smax %= mod
ans = (smax-smin)%mod
print(ans)