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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collection;
import java.util.LinkedList;
import java.util.List;
import java.util.Locale;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) throws IOException {
		new Thread(null, new Runnable() {
			public void run() {
				try {
					long prevTime = System.currentTimeMillis();
					new Main().run();
					System.err.println("Total time: "
							+ (System.currentTimeMillis() - prevTime) + " ms");
					System.err.println("Memory status: " + memoryStatus());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
		}, "1", 1L << 24).start();
	}

	void run() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		Object o = solve();
		if (o != null)
			out.println(o);
		out.close();
		in.close();
	}
	
	private Object solve() throws IOException {
		int n = ni();
		int k =ni();
		int p = ni();
		
		int[] arr = nia(n);
		
		LinkedList<Integer> even = new LinkedList<Integer>();
		LinkedList<Integer> odd = new LinkedList<Integer>();
		
		for(int a : arr)
			if(a%2==0){
				even.add(a);
			}else{
				odd.add(a);
			}
		List<Integer>[] ans = (List<Integer>[]) new List[k];
		for(int i =0;i<k;i++)
			ans[i]= new ArrayList<Integer>();
		
		for(int i =0;i<k-p;i++){
			if(odd.isEmpty())
				return "NO";
			ans[k-1-i].add(odd.pollFirst());
		}
		if(odd.size()%2==1)
			return "NO";
		
		int index =0;
		while(index<p && odd.size()>=2){
			ans[index].add(odd.pollFirst());
			ans[index].add(odd.pollFirst());
			index++;
		}
		while(index<p){
			if(even.isEmpty())
				return "NO";
			ans[index++].add(even.pollFirst());
		}
		ans[0].addAll(even);
		ans[0].addAll(odd);
		
		pln("YES");
		for(List<Integer> list : ans){
			p(list.size());
			for(int a : list)
				p(" "+a);
			pln();
		}
		return null;
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer strTok = new StringTokenizer("");

	String nextToken() throws IOException {
		while (!strTok.hasMoreTokens())
			strTok = new StringTokenizer(in.readLine());
		return strTok.nextToken();
	}

	int ni() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nl() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nd() throws IOException {
		return Double.parseDouble(nextToken());
	}

	int[] nia(int size) throws IOException {
		int[] ret = new int[size];
		for (int i = 0; i < size; i++)
			ret[i] = ni();
		return ret;
	}

	long[] nla(int size) throws IOException {
		long[] ret = new long[size];
		for (int i = 0; i < size; i++)
			ret[i] = nl();
		return ret;
	}

	double[] nda(int size) throws IOException {
		double[] ret = new double[size];
		for (int i = 0; i < size; i++)
			ret[i] = nd();
		return ret;
	}

	String nextLine() throws IOException {
		strTok = new StringTokenizer("");
		return in.readLine();
	}

	boolean EOF() throws IOException {
		while (!strTok.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null)
				return true;
			strTok = new StringTokenizer(s);
		}
		return false;
	}

	void printRepeat(String s, int count) {
		for (int i = 0; i < count; i++)
			out.print(s);
	}

	void printArray(int[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i > 0)
				out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}

	void printArray(long[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i > 0)
				out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}

	void printArray(double[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i > 0)
				out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}

	void printArray(double[] array, String spec) {
		for (int i = 0; i < array.length; i++) {
			if (i > 0)
				out.print(' ');
			out.printf(Locale.US, spec, array[i]);
		}
		out.println();
	}

	void printArray(Object[] array) {
		boolean blank = false;
		for (Object x : array) {
			if (blank)
				out.print(' ');
			else
				blank = true;
			out.print(x);
		}
		out.println();
	}

	@SuppressWarnings("rawtypes")
	void printCollection(Collection collection) {
		boolean blank = false;
		for (Object x : collection) {
			if (blank)
				out.print(' ');
			else
				blank = true;
			out.print(x);
		}
		out.println();
	}

	static String memoryStatus() {
		return (Runtime.getRuntime().totalMemory()
				- Runtime.getRuntime().freeMemory() >> 20)
				+ "/" + (Runtime.getRuntime().totalMemory() >> 20) + " MB";
	}

	public void pln() {
		out.println();
	}

	public void pln(int arg) {
		out.println(arg);
	}

	public void pln(long arg) {
		out.println(arg);
	}

	public void pln(double arg) {
		out.println(arg);
	}

	public void pln(String arg) {
		out.println(arg);
	}

	public void pln(boolean arg) {
		out.println(arg);
	}

	public void pln(char arg) {
		out.println(arg);
	}

	public void pln(float arg) {
		out.println(arg);
	}

	public void pln(Object arg) {
		out.println(arg);
	}

	public void p(int arg) {
		out.print(arg);
	}

	public void p(long arg) {
		out.print(arg);
	}

	public void p(double arg) {
		out.print(arg);
	}

	public void p(String arg) {
		out.print(arg);
	}

	public void p(boolean arg) {
		out.print(arg);
	}

	public void p(char arg) {
		out.print(arg);
	}

	public void p(float arg) {
		out.print(arg);
	}

	public void p(Object arg) {
		out.print(arg);
	}

}