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, K = map(int, input().split())
As = sorted(list(map(int, input().split())))

def getInvs(n, MOD):
    invs = [0] * (n+1)
    invs[1] = 1
    for x in range(2, n+1):
        invs[x] = (-(MOD//x) * invs[MOD%x]) % MOD
    return invs
invs = getInvs(N, MOD)

combiK = []
for i in range(K-1):
    combiK.append(0)
combiK.append(1)
for i in range(K, N+1):
    c = combiK[-1]
    combiK.append((c * i * invs[i-K+1]) % MOD)

ans = 0
for i, a in enumerate(As):
    ans -= a * combiK[N-i-1]
    ans += a * combiK[i]
    ans %= MOD
print(ans)