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()
fact = [1]
mod = 10**9+7
for i in range(1, N+1):
    fact.append(fact[i-1]*i % mod)
ifact = [None]*(N+1)
ifact[N] = pow(fact[N], mod-2, mod)
for i in range(N, 0, -1):
    ifact[i-1] = i*ifact[i] % mod
def comb(n,k):
    if n < k:
        return 0
    elif n == 0 or k == 0:
        return 1
    return (fact[n]*ifact[k]*ifact[n-k]) % mod
ans = 0
for i in range(N):
    ans -= comb(N-i-1, K-1)*A[i]
    ans += comb(i, K-1)*A[i]
    ans %= mod
print(ans)