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
def memfact(a,m):
    temp = 1
    yield temp
    for i in range(1,a+1):
        temp = temp * i % m
        yield temp
def comb(n,r,m):
    if r == 0: return 1
    return memf[n]*pow(memf[r],m-2,m)*pow(memf[n-r],m-2,m)

N,K,*a = map(int, open(0).read().split())
m = 1000000007
memf = []
mfappend = memf.append
for x in memfact(N-1,m):
    mfappend(x)
a.sort()
ans = 0
if K == 1:
    print(0)
else:
    for i in range(1,N-K+2):
        ans = (ans + a[-i] * comb(N-i,K-1,m)) % m
    for i in range(1,N-K+2):
        ans = (ans - a[i-1] * comb(N-i,K-1,m)) % m
    print(ans)