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.IOException;
import java.io.InputStream;
import java.util.*;

public class Main {
	static long mod = 1000000007;
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int n = sc.nextInt();
		int k = sc.nextInt();
		long[] a = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextLong();
		}
		Arrays.sort(a);
		long sum = 0;
		COMinit(n);
		for (int i = 1; i < n; i++) {
			sum += COM(n - i, k - 1) * (a[n - i] - a[i - 1]) % mod;
			sum %= mod;
		}
		if (sum < 0) {
			sum += mod;
		}
		System.out.println(sum);
	}

	static long[] fac;
	static long[] finv;
	static long[] inv;

	static void COMinit(int n) {
		fac = new long[n + 1];
		finv = new long[n + 1];
		inv = new long[n + 1];
		fac[0] = 1;
		fac[1] = 1;
		finv[0] = 1;
		finv[1] = 1;
		inv[1] = 1;
		for (int i = 2; i < n; i++) {
			fac[i] = fac[i - 1] * i % mod;
			inv[i] = mod - inv[(int) (mod % i)] * (mod / i) % mod;
			finv[i] = finv[i - 1] * inv[i] % mod;
		}
	}
	static long COM(int n, int k) {
		if (n < k || (n < 0 || k < 0)) {
			return 0;
		}
		return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() {
		if (hasNextByte()) {
			return buffer[ptr++];
		} else {
			return -1;
		}
	}
	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}
	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
			ptr++;
		}
		return hasNextByte();
	}
	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || Integer.MAX_VALUE < nl) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}