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 = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
a.sort()

def mod_nCr(n,k,mod):
    r = min(k,n-k)
    return fact[n]*factinv[k]*factinv[n-k]%mod

mod = 10**9+7
fact = [1,1]
inv = [0,1]
factinv = [1,1]
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(k-1,n)[::-1]:
    ans += a[i]*mod_nCr(i,k-1,mod)
    ans %= mod
a.reverse()
for i in range(k-1,n)[::-1]:
    ans -= a[i]*mod_nCr(i,k-1,mod)
    ans %= mod
print(ans%mod)