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()

sosu = 10 ** 9 + 7
fac = [1 for i in range(N)]
finv = [1 for i in range(N)]
inv = [1 for i in range(N)]
for i in range(2, N):
    fac[i] = fac[i-1] * i % sosu
    inv[i] = sosu - inv[sosu%i] * (sosu // i) % sosu
    finv[i] = finv[i-1] * inv[i] % sosu
ans = 0

for i in range(N-K+1):
    ans += (((((A[-i-1] - A[i]) * fac[N-1-i]) % sosu ) * finv[K-1]) % sosu ) * finv[N-i-K] % sosu
    ans = ans % sosu
print(ans)
