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
import sys
input = sys.stdin.readline

N,K=map(int,input().split())
A = list(map(int, input().split()))
A.sort()

def cmb(n, r, mod):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return (fact[n] * factinv[r] * factinv[n-r])%mod

mod=10**9 + 7
fact=[1,1]
factinv=[1,1]
inv=[0,1]
 
for i in range(2, N + 1):
    fact.append((fact[-1] * i) % mod)
    inv.append((-inv[mod % i] * (mod // i)) % mod)
    factinv.append((factinv[-1] * inv[-1]) % mod)
ans=0
for i in range(N-K+1):
    ans+=(A[-i-1]-A[i])*cmb(N-i-1,K-1,mod)
    ans%=mod
print(ans)