p02804 AtCoder Beginner Contest 151 - Max-Min Sums
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
```python
N,K = map(int,input().split())
A = list(map(int,input().split()))

mod = 10**9+7

A = sorted(A)

bikkuri = [1]
for i in range(1,N+1):
    bikkuri.append((bikkuri[-1]*i)%mod)
bikkuri2 = [1]
for i in range(1,N+1):
    bikkuri2.append(pow(bikkuri[i],mod-2,mod))
    
def comb(n,r):
    if n<r:
        return 0
    else:
        return (bikkuri[n]*bikkuri2[n-r]*bikkuri2[r])%mod
    
ans = 0
for i in range(N):
    ans += A[i]*(comb(i,K-1)-comb(N-i-1,K-1))
    ans %= mod
print(ans)
```