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 = map(int, input().split())
MOD = 10**9+7
A = [a % MOD for a in sorted(list(map(int, input().split())))]
MIN, MAX = 0, 0

def div_MOD(a):     # (a^{-1} mod MOD) をフェルマーの小定理より求める
    return pow(a, MOD - 2, MOD)     # a^{-1} = a^{p-2} (mod p)

C = [0]*(K-1) + [1]
for n in range(K, N):
    C.append((C[n-1] * n * div_MOD(n-(K-1))) % MOD)

for i in range(N-K+1):
    MIN = (MIN + (A[i] * C[N-i-1]) % MOD) %MOD
for i in range(N-K+1):
    MAX = (MAX + (A[N-1-i] * C[N-i-1]) % MOD) %MOD

print((MAX - MIN) % MOD)