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
import java.io.*;
import java.util.*;

public class Main {

    private static FastReader in = new FastReader(System.in);
    private static PrintWriter out = new PrintWriter(System.out);

    private static final long MOD = (long) 1e9 + 7;

    public static void main(String[] args) {
        solve();
        out.flush();
    }

    private static void solve() {
        ModCalculator calc = new ModCalculator(MOD);

        int n = in.nextInt();
        int k = in.nextInt();
        int[] a = in.nextIntArray(n);
        Arrays.sort(a);

        long[] cum = new long[n + 1];
        for (int i = 0; i < a.length; i++) {
            cum[i + 1] = cum[i] + a[i];
        }

        long ans = 0;
        calc.populate(n);

        // + (1 * (a[K] + a[K + 1] + ... + a[N]) + comb(K - 1, 1) * (a[K + 1] + a[K + 2] + ... + a[N]) + ... + comb(N - 2, N - K) * a[N])
        // - (1 * (a[1] + a[2] + ... + a[N - K + 1]) + comb(K - 1, 1) * (a[1] + a[2] + ... + a[N - K]) + ... + comb(N - 2, N - K) * a[1])
        for (int i = 0; i <= n - k; i++) {
            ans = calc.add(
                    ans,
                    calc.multiply(
                            calc.combination(k - 2 + i, i),
                            calc.subtract(calc.subtract(cum[n], cum[k - 1 + i]), cum[n - k + 1 - i])
                    )
            );
        }

        out.println(ans);
    }

    private static class ModCalculator {
        private final long mod;

        // factorial in mod
        // factMod[1] = 1, factMod[2] = 2, ...
        private List<Long> factorial;
        // inverse factorial in mod
        private List<Long> inverseFactorial;

        ModCalculator(long mod) {
            this.mod = mod;
            factorial = new ArrayList<>();
            inverseFactorial = new ArrayList<>();
            factorial.add(1L);
            inverseFactorial.add(1L);
        }

        /**
         * Quickly populate factorial and inverse factorial up to n
         */
        private void populate(int n) {
            // i == next index
            int start = factorial.size();
            for (int i = start; i <= n; i++) {
                factorial.add(
                        multiply(factorial.get(i - 1), i)
                );
                // temporarily add
                inverseFactorial.add(0L);
            }
            // avoid inverse calculation by filling inverseFactorial in the inverse direction
            inverseFactorial.set(n, inverse(factorial.get(n)));
            for (int i = n; i > start; i--) {
                inverseFactorial.set(i - 1, multiply(inverseFactorial.get(i), i));
            }
        }

        // a + b (mod m)
        long add(long a, long b) {
            return (a + b) % mod;
        }

        // a - b (mod m)
        long subtract(long a, long b) {
            return add(add(a, -b), mod);
        }

        // a * b (mod m)
        long multiply(long a, long b) {
            return (a * b) % mod;
        }

        // x^-1 (mod m)
        long inverse(long x) {
            return power(x, mod - 2);
        }

        // x^n (mod m)
        long power(long x, long n) {
            long ans = 1;
            while (n != 0) {
                if ((n & 1) == 1L) ans = multiply(ans, x);
                x = multiply(x, x);
                n = n >> 1;
            }
            return ans;
        }

        /**
         * Calculates factorial value in mod.
         */
        long factorial(int n) {
            populate(n);
            return factorial.get(n);
        }

        /**
         * Calculates inverse factorial value in mod.
         */
        long inverseFactorial(int n) {
            populate(n);
            return inverseFactorial.get(n);
        }

        /**
         * Calculates combination value in mod.
         * <br>a.k.a
         * <br>aCb
         * <br> = n! / (n - r)! r!
         */
        long combination(int n, int r) {
            if (n == 0 && r == 0) return 1;
            if (n < r || n < 0) return 0;

            populate(n);
            return multiply(factorial.get(n), multiply(inverseFactorial.get(n - r), inverseFactorial.get(r)));
        }

        /**
         * Calculates multi-choose, or combination with repetition in mod.
         * <br>a.k.a
         * <br>nHr
         */
        long multiChoose(int n, int r) {
            return combination(n + r - 1, r);
        }

        /**
         * Calculates permutation value in mod.
         * <br>a.k.a
         * <br>aPb
         * <br> = n! / (n - r)!
         */
        long permutation(int n, int r) {
            if (n == 0 && r == 0) return 0;
            if (n < r || n < 0) return 0;

            populate(n);
            return multiply(factorial.get(n), inverseFactorial.get(n - r));
        }
    }

    // https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader(InputStream inputStream) {
            br = new BufferedReader(new
                    InputStreamReader(inputStream));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException  e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        // https://qiita.com/masakinpo/items/5f77f2a879578a85a0bb
        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }
}
