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;
typedef long long ll;
const int N = 200007, M = 1e9 + 7;
ll v[N], fat[N];


ll fast_pow(ll a, ll b) {
    ll ans = 1;
    while(b) {
        if(b&1) ans = (ans * a)%M;
        b >>= 1;
        a = a * a % M;
    }
    return ans;
}
ll choose(ll n, ll k) {
    if(k > n or k < 0) return 0;
    ll den = fat[n-k] * fat[k] % M;
    return fat[n] * fast_pow(den, M - 2) % M;
}

int main() {
    int n, k; cin >> n >> k;

    fat[0] = 1;
    for(int i = 1; i <= 2 * n; ++i) fat[i] = fat[i-1] * i % M;
    for(int i = 0; i < n; ++i) cin >> v[i];
    sort(v, v + n);

    ll ans = 0;
    // soma
    for(int i = 0; i < n; ++i) {
        ll aux = v[i] * choose(i, k-1) % M;
        ans = (ans + aux)%M;
    }

    // subtrair
    for(int i = 0; i < n; ++i) {
        ll aux = v[i] * choose(n - i - 1, k-1) % M;
        ans = (ans - aux + M)%M;
    }

    cout << ans << endl;
}