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
using namespace std;
constexpr int mod=1e9+7;
int fact_arr[100001];
int fact(int n){
    if(fact_arr[n]!=0)
        return fact_arr[n];
    if(n==0)
        return fact_arr[n]=1;
    return fact_arr[n]=fact(n-1)*n%mod;
}
int pow(int x,int n){
    int ret=1;
    while(n){
        if(n&1)
            (ret*=x)%=mod;
        (x*=x)%=mod;
        n>>=1;
    }
    return ret;
}
int inv(int n){
    return pow(n,mod-2);
}
int comb(int n,int k){
    if(k>n)
        return 0;
    return fact(n)*inv(fact(k)*fact(n-k)%mod)%mod;
}
signed main(){
    int n,k,a[100000];
    cin>>n>>k;
    for(int i=0;i<n;i++)
        cin>>a[i];
    sort(a,a+n);
    int ans=0;
    for(int i=0;i<n;i++)
        (ans+=comb(i,k-1)*(a[i]-a[n-1-i]))%=mod;
    cout<<ans<<endl;
}
