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 {
	public static void main(String[] args) {
		FastScanner fs = new FastScanner();
		int n = fs.nextInt();
		int k = fs.nextInt();
		Mod.pre_factrials(n);
		ArrayList<Integer> a = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			a.add(fs.nextInt());
		}
		Collections.sort(a);
		long ans = 0;
		for (int i = 0; i < n; i++) {
			ans = Mod.plus(ans, Mod.sub(Mod.mul(a.get(i), Mod.fastFermatComb(i, k - 1)),
					Mod.mul(a.get(i), Mod.fastFermatComb(n - i - 1, k - 1))));
		}
		System.out.println(ans);
	}

	static class Mod {
		// べき乗とコンビネーションの余りを計算
		// 下のmodの値を法としたい値にする
		// コンビネーションを使う前にpre_factrials()の引数を使用する最大値にして宣言しておく
		static int mod = 1000000007;
		// Fast Fermat Combination
		static long factorials[];
		static long factorialDivs[];

		static void pre_factrials(int n) {
			factorials = new long[n + 1];
			factorialDivs = new long[n + 1];// 割算の結果を格納する配列
			factorials[0] = 1;
			for (int i = 0; i < n; i++) {
				factorials[i + 1] = mul(i + 1, factorials[i]);
			}
			factorialDivs[n] = div(1, factorials[n]);// 最初に1/(n!)を求める事で、1/(n-1)!からは掛け算で求める事ができる。
			for (int i = n - 1; i >= 0; i--) {
				factorialDivs[i] = mul(factorialDivs[i + 1], i + 1);
			}
		}

		static long modpow(long a, long p) {
			long r = 1;
			for (; p > 0; p = p >> 1) {
				if ((p & 1) > 0) {
					r = r * a % mod;
				}
				a = a * a % mod;
			}
			return r;
		}

		static long fastFermatComb(int a, int b) {
			if (factorials.length == 0)
				System.err.println("error : factorials has not been culculated!! do [pre_factorial] method");
			if (a < b) {
				return 0;
			}
			long af = factorials[a];
			long bf = factorialDivs[b];
			long abf = factorialDivs[a - b];
			long res = mul(mul(af, bf), abf);
			return res;
		}

		static long plus(long x, long y) {
			x %= mod;
			y %= mod;
			long res = (x + y) % mod;
			return res;
		}

		static long sub(long x, long y) {
			x %= mod;
			y %= mod;
			long res = (x - y + mod) % mod;
			return res;
		}

		static long mul(long x, long y) {
			x %= mod;
			y %= mod;
			long res = x * y % mod;
			return res;
		}

		static long div(long x, long y) {
			x %= mod;
			y %= mod;
			long res = x * modpow(y, mod - 2) % mod;
			return res;
		}

	}

}

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 || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}

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