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
def main():
    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, n+1):
        fact.append(fact[-1]*i % mod)

    def inv_n(n, mod=10**9+7): return pow(n, mod-2, mod)
    def nCr(n, r, mod=10**9+7): return inv_n(fact[n-r]
                                             * fact[r] % mod, mod)*fact[n] % mod

    ans = 0

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


main()
