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 = [int(a) for a in input().split()]
A = [int(a) for a in input().split()]
p = 10 ** 9 + 7
list.sort(A)


binom = 1 # (k-1) choose (k-1)
ans = binom * (A[K - 1] - A[N - K]) % p #
inv = [0, 1]    # inv[i] : inverse of i mod p

# (i choose k-1) = (i-1 choose k-1) * i / (i-k+1)
for i in range(2, N):
    if i <= N - K:
        inv.append(( inv[p % i] * (p - p // i) ) % p )

    if i >= K:
        binom = (((i * inv[i - K + 1]) % p) * binom ) % p # i choose (k-1)
        ans = (ans + binom * (A[i] - A[N - 1 - i])) % p

print(ans)
