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 = 123456
MOD = (10 ** 9) + 7

fs = [1 for i in xrange(N)]
for i in xrange(1, N):
    fs[i] = fs[i - 1] * i % MOD

n, k = map(int, raw_input().split())
ns = map(int, raw_input().split())
ns.sort()

def fermat(u):
    return pow(u, MOD - 2, MOD)

def C(a, b):
    if b > a:
        return 0
    if b == 0:
        return 0
    assert a - b >= 0
    res = fs[a] * fermat(fs[b]) % MOD * fermat(fs[a - b]) % MOD
    return res % MOD

assert C(5, 3) == 10

res = 0
for i in xrange(n):
    res += C(i, k - 1) * ns[i] % MOD
    res %= MOD
    res -= C(n - i - 1, k - 1) * ns[i] % MOD
    res = ((res % MOD) + MOD) % MOD

print res
