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 MAXN 233333
using namespace std; 

typedef long long LL;
const LL MOD = 1e9+7;
LL a[MAXN],s[MAXN],ga[MAXN],ans,k;
LL n;
LL qpow(LL a,LL x){
	if(x==0){
		return 1;
	}
	LL t = qpow(a,x/2)%MOD;
	if(x%2==0){
		return (t*t)%MOD;
	}
	else
		return (((t*t)%MOD)*a)%MOD;
}
LL rev(LL x){
	return qpow(x,MOD-2);
} 
LL calc(LL x,LL y){
	//if(!y) return 1;
	if(x<y) return 0;
	else return (((ga[x]*rev(ga[y]))%MOD)*rev(ga[x-y]))%MOD;
}
int main()
{
	cin>>n>>k;
	for(int i = 1;i<=n;i++)
		cin>>a[i];
	sort(a+1,a+1+n);
	for(int i = 1;i<=n;i++){
		s[i] = (a[i] + s[i-1])%MOD; 
		ga[i] = (i==1?1:(ga[i-1]*i)%MOD); 
	}
	ga[0] = 1;
	for(LL i = 1;i<=n-1;i++){
		LL w = calc(i-1,k-2);
		ans += w*(s[n]-s[n-i]-s[i]);
		ans %= MOD;
	} 
	cout<<ans;
}