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
#include<bits/stdc++.h>
using namespace std;
#define ll long long

ll a[100009], mod = 1e9+7;

ll bigmod(ll b, ll p)
{
    if(p == 0)
        return 1;
    ll x = 1, y;
    if(p&1)
        x = b%mod;
    y = bigmod(b, p>>1);
    return ((y*y)%mod*x)%mod;
}



int main()
{
    ll n, k, i, j;
    cin >> n >> k;
    for(i = 0; i < n; i++)
        cin >> a[i];
    sort(a, a+n);
    ll p = 1, ans = a[k-1] - a[n-k];
    for(i = k; i <= n-1; i++)
    {
        p = (p*(i*bigmod(i-k+1, mod-2)%mod))%mod;
        ans = (ans + p*(a[i] - a[n - i - 1])%mod)%mod;
    }

    cout << (ans + mod)%mod;
}
