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

A.sort()

factorial = [1]
for i in range(1, N + 1):
    factorial.append(factorial[-1] * i  % MOD)
inv_factorial = [-1] * (N + 1)
inv_factorial[-1] = pow(factorial[-1], MOD - 2, MOD)
for i in reversed(range(N)):
    inv_factorial[i] = inv_factorial[i + 1] * (i + 1) % MOD


ans = 0
for i in range(N - K + 1):
    c = factorial[N - 1 - i] * inv_factorial[K - 1] * inv_factorial[N - K - i]
    ans += c * (A[-1 - i] - A[i])
    ans %= MOD

print(ans)
