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
MOD = 10**9 + 7

N, K = map(int, raw_input().split())
A = map(int, raw_input().split())

factorial = [1]
for i in range(1, N+1):
    factorial.append((i * factorial[-1]) % MOD)

def nCk(n, k):
    numerator = factorial[n]
    denominator = factorial[n-k] * factorial[k]
    return numerator * pow(denominator, MOD - 2, MOD)

ans = 0

A.sort()
for i in range(N-K+1):
    best = A[i]
    contribution = (best * nCk(N-i-1, K-1))
    ans = (ans - contribution) % MOD

A = A[::-1]
for i in range(N-K+1):
    best = A[i]
    contribution = (best * nCk(N-i-1, K-1))
    ans = (ans + contribution) % MOD

print ans
