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 = [int(i) for i in input().split()]
a = [int(i)for i in input().split()]
mod = 10**9+7
a.sort()
fact = [1]*(n+2)
inv = [1]*(n+2)
for i in range(2,n+2):
    fact[i]=(fact[i-1]*i)%mod
inv[n+1]=pow(fact[n+1],mod-2,mod)
for i in range(n,1,-1):
    inv[i] = (inv[i+1]*(i+1))%mod

ans = 0
for i in range(n-1,k-2,-1):
    ans = (ans + (((fact[i]*inv[i-k+1]*inv[k-1])%mod)*a[i])%mod)%mod
for i in range(n-k+1):
    N = n-1-i
    K = k-1
    ans = (ans - (((fact[N]*inv[N-K]*inv[K])%mod)*a[i])%mod)%mod
print(ans)