Problem: General Payne has a battalion of n soldiers. The soldiers' beauty contest is coming up, it will last for k days. Payne decided that his battalion will participate in the pageant. Now he has choose the participants.

All soldiers in the battalion have different beauty that is represented by a positive integer. The value ai represents the beauty of the i-th soldier.

On each of k days Generals has to send a detachment of soldiers to the pageant. The beauty of the detachment is the sum of the beauties of the soldiers, who are part of this detachment. Payne wants to surprise the jury of the beauty pageant, so each of k days the beauty of the sent detachment should be unique. In other words, all k beauties of the sent detachments must be distinct numbers.

Help Payne choose k detachments of different beauties for the pageant. Please note that Payne cannot just forget to send soldiers on one day, that is, the detachment of soldiers he sends to the pageant should never be empty.

Input

The first line contains two integers n, k (1 ≤ n ≤ 50; 1 ≤ k ≤  <image>) — the number of soldiers and the number of days in the pageant, correspondingly. The second line contains space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 107) — the beauties of the battalion soldiers.

It is guaranteed that Payne's battalion doesn't have two soldiers with the same beauty.

Output

Print k lines: in the i-th line print the description of the detachment that will participate in the pageant on the i-th day. The description consists of integer ci (1 ≤ ci ≤ n) — the number of soldiers in the detachment on the i-th day of the pageant and ci distinct integers p1, i, p2, i, ..., pci, i — the beauties of the soldiers in the detachment on the i-th day of the pageant. The beauties of the soldiers are allowed to print in any order.

Separate numbers on the lines by spaces. It is guaranteed that there is the solution that meets the problem conditions. If there are multiple solutions, print any of them.

Examples

Input

3 3
1 2 3


Output

1 1
1 2
2 3 2


Input

2 1
7 12


Output

1 12 

Solution (in JAVA):

Solution:
import java.io.BufferedWriter;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Random;

/**
 * Actual solution is at the top, in class Solver
 */
final public class Main implements Runnable {
	private static String[] args;

	public static void main(String[] args) {
		Main.args = args;
		new Thread(null, new Main(), "MyRunThread", 1 << 27).start();
	}

	@Override
	public void run() {
		long time_beg = -1;
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		if (args.length > 0 && args[0].equals("outside")) {
			time_beg = System.currentTimeMillis();
			try {
				inputStream = new FileInputStream("IO/in.txt");
//				outputStream = new FileOutputStream("IO/out.txt");
			} catch (Exception e) {
				System.err.println(e);
				System.exit(1);
			}
		} else {
			try {
//				inputStream = new FileInputStream("input.txt");
//				outputStream = new FileOutputStream("output.txt");
			} catch (Exception e) {
				System.err.println(e);
				System.exit(1);
			}
		}

		Solver s = new Solver();
		s.in = new InputReader(inputStream);
		s.out = new OutputWriter(outputStream);
		if (args.length > 0 && args[0].equals("outside")) {
			s.dout = new DebugWriter(s.out);
		}

		s.solve();

		if (args.length > 0 && args[0].equals("outside")) {
			s.dout.printFormat("*** Total time: %.3f ***\n", (System.currentTimeMillis() - time_beg) / 1000.0);
		}

		s.out.close();
	}
}

final class Solver {
	InputReader in;
	OutputWriter out;
	DebugWriter dout;

	public void solve() {
		int n = in.readInt();
		int k = in.readInt();
		int[] mas = new int[n];
		for (int i = 0; i < n; ++i)
			mas[i] = in.readInt();

		Arrays.sort(mas);

		for (int j = n - 1; j >= 0; --j) {


			for (int i = 0; i <= j; ++i) {
				out.print(n - 1 - j + 1);
				for (int ii = n - 1; ii > j; --ii)
					out.print(" " + mas[ii]);
				out.printLine(" " + mas[i]);
				--k;
				if (k == 0) return;
			}
		}

	}
}

final class InputReader {
	private boolean finished = false;

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	private int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int peek() {
		if (numChars == -1)
			return -1;
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				return -1;
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar];
	}

	public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public long readLong() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public String readString() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public static boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private String readLine0() {
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != '\n' && c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = read();
		}
		return buf.toString();
	}

	public String readLine() {
		String s = readLine0();
		while (s.trim().length() == 0)
			s = readLine0();
		return s;
	}

	public String readLine(boolean ignoreEmptyLines) {
		if (ignoreEmptyLines)
			return readLine();
		else
			return readLine0();
	}

	public BigInteger readBigInteger() {
		try {
			return new BigInteger(readString());
		} catch (NumberFormatException e) {
			throw new InputMismatchException();
		}
	}

	public char readCharacter() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		return (char) c;
	}

	public double readDouble() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		double res = 0;
		while (!isSpaceChar(c) && c != '.') {
			if (c == 'e' || c == 'E')
				return res * Math.pow(10, readInt());
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		}
		if (c == '.') {
			c = read();
			double m = 1;
			while (!isSpaceChar(c)) {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}

	public boolean isExhausted() {
		int value;
		while (isSpaceChar(value = peek()) && value != -1)
			read();
		return value == -1;
	}
}

final class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}


	public void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(Object... objects) {
		print(objects);
		writer.println();
	}

	public void printFormat(String format, Object... objects) {
		writer.printf(format, objects);
	}


	public void print(char[] objects) {
		writer.print(objects);
	}

	public void printLine(char[] objects) {
		writer.println(objects);
	}

	public void printLine(char[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(int[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(int[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(int[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(short[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(short[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(short[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(long[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(long[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(long[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(double[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(double[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(double[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(byte[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(byte[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(byte[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(boolean[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(boolean[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(boolean[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void close() {
		writer.close();
	}

	public void flush() {
		writer.flush();
	}
}

final class DebugWriter {
	private final OutputWriter writer;

	public DebugWriter(OutputWriter writer) {
		this.writer = writer;
	}

	private void printDebugMessage() {
		writer.print("DEBUG:\t");
	}


	public void printLine(Object... objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printFormat(String format, Object... objects) {
		flush();
		printDebugMessage();
		writer.printFormat(format, objects);
		flush();
	}


	public void printLine(char[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(char[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(double[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(double[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(int[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(int[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(short[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(short[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(long[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(long[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(byte[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(byte[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void printLine(boolean[] objects) {
		flush();
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(boolean[][] objects) {
		flush();
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}


	public void flush() {
		writer.flush();
	}
}