Problem: Devu being a small kid, likes to play a lot, but he only likes to play with arrays. While playing he came up with an interesting question which he could not solve, can you please solve it for him?

Given an array consisting of distinct integers. Is it possible to partition the whole array into k disjoint non-empty parts such that p of the parts have even sum (each of them must have even sum) and remaining k - p have odd sum? (note that parts need not to be continuous).

If it is possible to partition the array, also give any possible way of valid partitioning.

Input

The first line will contain three space separated integers n, k, p (1 ≤ k ≤ n ≤ 105; 0 ≤ p ≤ k). The next line will contain n space-separated distinct integers representing the content of array a: a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

In the first line print "YES" (without the quotes) if it is possible to partition the array in the required way. Otherwise print "NO" (without the quotes).

If the required partition exists, print k lines after the first line. The ith of them should contain the content of the ith part. Print the content of the part in the line in the following way: firstly print the number of elements of the part, then print all the elements of the part in arbitrary order. There must be exactly p parts with even sum, each of the remaining k - p parts must have odd sum.

As there can be multiple partitions, you are allowed to print any valid partition.

Examples

Input

5 5 3
2 6 10 5 9


Output

YES
1 9
1 5
1 10
1 6
1 2


Input

5 5 3
7 14 2 9 5


Output

NO


Input

5 3 1
1 2 3 7 5


Output

YES
3 5 1 3
1 7
1 2

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.LinkedList;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main
{

	public static void main(String[] args) throws IOException
	{

		Main main = new Main();
		main.read();
	}

	/* IO */
	private InputReader in;
	private StringBuilder ans;

	/* fields */
	private int n;
	private int k;
	private int nEven;
	private int[] arr;

	private void read() throws IOException
	{
		// streams
		boolean file = false;
		if (file)
			in = new InputReader(new FileInputStream("Input.txt"));
		else
			in = new InputReader(System.in);
		ans = new StringBuilder();

		// read
		n = Integer.parseInt(in.next());
		k = Integer.parseInt(in.next());
		nEven = Integer.parseInt(in.next());
		arr = new int[n];
		for (int i = 0; i < n; i++)
			arr[i] = Integer.parseInt(in.next());

		// solve
		System.out.println(solve());

	}

	private String solve()
	{
		// classify numbers
		Stack<Integer> odd = new Stack<>();
		Stack<Integer> even = new Stack<>();
		for (int i = 0; i < n; i++)
			if (arr[i] % 2 == 0)
				even.push(arr[i]);
			else
				odd.push(arr[i]);

		// make odd partitions
		LinkedList<LinkedList<Integer>> partitions = new LinkedList<>();
		int nOdd = k - nEven;
		for (int i = 0; i < nOdd; i++)
		{
			if (odd.isEmpty())
				return "NO";
			LinkedList<Integer> l = new LinkedList<>();
			l.push(odd.pop());
			partitions.add(l);
		}

		// make even
		for (int i = 0; i < nEven; i++)
		{
			LinkedList<Integer> l = new LinkedList<>();
			if (even.size() > 0)
			{
				l.add(even.pop());
			} else if (odd.size() >= 2)
			{
				l.add(odd.pop());
				l.add(odd.pop());
			} else
				return "NO";
			partitions.add(l);
		}

		// add the rest to any partition
		long sum = 0;
		while (!odd.isEmpty())
		{
			int x = odd.pop();
			sum += x;
			partitions.getFirst().add(x);
		}
		while (!even.isEmpty())
		{
			int x = even.pop();
			sum += x;
			partitions.getFirst().add(x);
		}
		if (sum % 2 == 1)
			return "NO";

		// form the answer
		StringBuilder strb = new StringBuilder();
		strb.append("YES\n");
		for (LinkedList<Integer> partition : partitions)
			strb.append(toString(partition) + "\n");
		return strb.toString();
	}

	private Object toString(LinkedList<Integer> partition)
	{
		StringBuilder strb = new StringBuilder();
		strb.append(partition.size());
		for (Integer x : partition)
			strb.append(" " + x);
		return strb.toString().trim();
	}

}

class InputReader
{
	public BufferedReader reader;
	public StringTokenizer tokenizer;

	public InputReader(InputStream stream)
	{
		reader = new BufferedReader(new InputStreamReader(stream), 32768);
		tokenizer = null;
	}

	public String next()
	{
		while (tokenizer == null || !tokenizer.hasMoreTokens())
		{
			try
			{
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e)
			{
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

}