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, *A = map(int, open(0).read().split())

MOD = 10 ** 9 + 7

fac = [0] * (N + 1)
fac[0] = 1
fac[1] = 1
for i in range(2, N + 1):
    fac[i] = fac[i - 1] * i % MOD

finv = [0] * (N + 1)
finv[N] = pow(fac[N], MOD - 2, MOD)
for i in reversed(range(1, N + 1)):
    finv[i - 1] = finv[i] * i % MOD

def comb(n, k):
    if n < k:
        return 0
    return fac[n] * finv[k] * finv[n - k] % MOD

ans = 0
for i, a in enumerate(sorted(A, reverse=True)):
    ans += a * comb(N - i - 1, K - 1)
    ans -= a * comb(i, K - 1)
    ans %= MOD
    
print(ans)
