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()
mod = 10**9+7
ans = 0
cmb = [0]*N
x = [0]*N
cmb[K-1] = 1
def Pow(a, n):
    if n == 0: return 1
    if n%2 == 0:
        return (Pow(a, n//2))**2%mod
    else:
        return Pow(a, n-1)*a%mod
for i in range(1,N-K+1):
    x[i] = Pow(i, mod-2)
    
for i in range(K, N):
    cmb[i] = cmb[i-1]*i%mod*x[i-K+1]%mod
for i in range(N):
    fac = cmb[i] - cmb[N-i-1]
    num = fac*a[i]%mod
    ans += num
    ans = ans%(10**9+7)
print(ans)