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
#abc_151_e
n,k = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
a.sort()

mod = 10**9 + 7

ans = 0

#precalculation of the factorial
#fact[i] = i!
num = 10**5 + 1
fact = [0] * num
fact[0] = 1
for i in range(1,num):
    fact[i] = (fact[i-1] * i) % mod
    
for i in range(k-1, n):
    f = fact[i] * pow(fact[k-1]*fact[i-k+1], mod-2, mod)
    ans += (a[i] * f) % mod
    
for i in range(0, n-k+1):
    f = fact[n-i-1] * pow(fact[k-1]*fact[n-k-i], mod-2, mod)
    ans -= (a[i] * f) % mod
    
print(ans%mod)
    
    