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 = 10 ** 5 + 1
fact = [1] * (N + 1)
ifact = [1] * (N + 1)

for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % mod
    ifact[i + 1] = pow(fact[i + 1], mod - 2, mod)


def comb(x, y):
    if y < 0 or y > x:
        return 0
    return (fact[x] * ifact[x - y] * ifact[y]) % mod


n, k = map(int, input().split())
a = sorted(list(map(int, input().split())))
ar = sorted(a, reverse=True)

ans = 0
for i in range(k - 1, n):
    ans += a[i] * comb(i, k - 1) % mod
    ans -= ar[i] * comb(i, k - 1) % mod
    ans %= mod

print(ans)
