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 = list(map(int,input().split()))
a.sort()
p = [1]
mod = 10**9+7
for i in range(n):
    p.append(p[-1]*(i+1)%mod)
p.pop()
def comb(n,k,mod):
    s = p[n]*pow(p[k],mod-2,mod)%mod
    s = s*pow(p[n-k],mod-2,mod)%mod
    return s
max_sum = 0
min_sum = 0
for i in range(n-k+1):
    max_sum += a[-(i+1)]*comb(n-1-i,k-1,mod)
    max_sum = max_sum%mod
    min_sum += a[i]*comb(n-1-i,k-1,mod)
    min_sum = min_sum%mod
ans = max_sum-min_sum
if ans < 0:
    ans += mod
print(ans)