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>
#define int long long
#define mod 1000000007
#define for0(i, n) for(int i = 0; i < (n); i++)
using namespace std;
int a[123456], n, k, ans = 0;
int f1(int a, int p) {
	if (p == 1)return a;
	if (p % 2)return f1(a, p - 1) * a % mod;
	else return f1(a * a % mod, p / 2) % mod;
}
signed main() {
	cin >> n >> k;
	for0(i, n)cin >> a[i]; sort(a, a + n);
	int p = 1;
	for0(i, n - k + 1) {
		ans += p * (a[k - 1 + i] - a[n - k - i]);
		ans %= mod;
		p *= k + i; p %= mod;
		p *= f1(1 + i, mod - 2); p %= mod;
	}
	cout << ans << endl;
}