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()))
mod = 10**9+7
def modinv(a, mod=10**9+7):
    return pow(a, mod-2, mod)

fac = [0]*(N+1)
fac[0] = 1
fac[1] = 1
for i in range(2,N+1):
    fac[i] = fac[i-1] * i % mod

def combi(n,r,mod=10**9+7):
    return( ( fac[n] * modinv(fac[r]) )%mod * modinv(fac[n-r]) % mod)

A.sort()
ans = 0
for i in range(1, N-K+2):
    ans += combi(N-i, K-1)*A[N-i] % mod
    ans += mod
    ans -= combi(N-i, K-1)*A[i-1] % mod

print(ans%mod)