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 cmb(n, r, mod):
    if (r < 0 or r > n):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod
 
mod = 10**9+7  
nums = 10**5 # 制約に合わせよう
g1, g2, inverse = [1, 1] , [1, 1], [0, 1]
 
for num in range(2, nums + 1):
    g1.append((g1[-1] * num) % mod)
    inverse.append((-inverse[mod % num] * (mod//num)) % mod)
    g2.append((g2[-1] * inverse[-1]) % mod)

n, k = map(int, input().split())
a = list(map(int, input().split()))
a.sort()

ans = 0
for i in range(n):
    res = cmb(n-i-1, k-1, mod)
    ans += res*a[n-i-1] - res*a[i]
    ans %= mod
print(ans)