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 = list(map(int, input().split()))
a.sort()
MOD = 10**9 + 7

fact = [1]

for i in range(1, 110000):
    fact.append(fact[-1] * i % MOD)

def rev(x):
    return pow(x, MOD-2, MOD)
    
def c(i, k):
    if(i < k):return 0
    return fact[i] * rev(fact[k]) * rev(fact[i-k]) % MOD

def calc():
    result = 0
    for i in range(n):
        result += a[i] * c(i, k-1)
        result %= MOD
    return result

ans = calc()
a = a[::-1]

ans -= calc()
ans %= MOD
if ans < 0:ans += MOD

print(ans)