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

mod = 10**9+7
N, K = map(int, input().split())
A = [0] + sorted(list(map(int, input().split())))
factorial = [1] * (N+1)
factorial_inv = [1] * (N+1)
for i in range(1, N+1):
    factorial[i] = factorial[i-1] * i % mod
    factorial_inv[i] = mod_inverse(factorial[i], mod)

ans = 0
for i in range(K, N+1):
    ans = (ans + factorial[i-1] * factorial_inv[i-K] * A[i]) % mod

for i in range(1, N-K+2):
    ans = (ans - factorial[N-i] * factorial_inv[N-K-i+1] * A[i]) % mod

ans = ans * factorial_inv[K-1] % mod
print(ans)
