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()

M = 10**9+7

def pow(a,b,M):
    if b == 0:
        return 1
    elif b % 2 == 0:
        return pow((a**2)%M,b//2,M) % M
    else:
        return ((a % M) * pow((a**2)%M,b//2,M)) % M

def inv(a,p):
    return pow(a,p-2,p)

ans,comb = 0,1
#i番目ではcomb = (K-1-i)_C_(K-1)
#max,min以外での選ぶ個数は常にK-1であることに注目すればcomb関数はいらなかった
for i in range(N-K+1):
    if i > 0:
        comb = (comb * (K-1+i) * inv(i,M)) % M
    ans = (ans + comb*((A[K-1+i]-A[N-K-i]) % M)) % M
print(ans)
