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 = [int(i) for i in input().split()]
a.sort()
total = 0
def cmb(n, r, mod):
    if (r<0 or r>n):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7
N = 10**5
g1 = [1,1]
g2 = [1,1]
inverse = [0,1]

for i in range(2, N + 1):
    g1.append((g1[-1]*i) % mod)
    inverse.append((-inverse[mod%i] * (mod//i)) % mod)
    g2.append((g2[-1]*inverse[-1]) % mod)

for i in range(n-k+1):
    total += cmb(n-i-1,k-1,mod)*(a[n-i-1]-a[i])
    total %= mod
print(total)