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 <iostream>
#include <cstdio>
#include <algorithm>
#define N 100005
using namespace std;

typedef long long ll;
ll M = 1e9 + 7;
ll n, k, s, a[N];
ll fac[N]{1, 1}, inv[N]{1, 1}, fiv[N]{1, 1};

ll com(ll p, ll q) {
	if (p < q) return 0;
	return fac[p] * fiv[p - q] % M * fiv[q] % M;
}

int main()
{
	ll i;
	cin >> n >> k;
	for (i = 2; i <= n; i++) {
		fac[i] = fac[i - 1] * i % M;
		inv[i] = inv[M % i] * (M - M / i) % M;
		fiv[i] = fiv[i - 1] * inv[i] % M;
	}
	for (i = 0; i < n; i++) scanf("%lld", &a[i]);
	sort(a, a + n);
	for (i = 0; i < n; i++) {
		s = (s + a[i] * (com(i, k - 1) - com(n - i - 1, k - 1))) % M;
	}
    cout << s << endl;
    return 0;
}