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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

// Note that at the actual CodeForces contest,
// - must use the default package
// - can use any class name
public class CF251Div2C {
	
	void solve(int n, int K, int p, int[] a) {
		int[] odds = new int[n];
		int[] evens = new int[n];
		int odd = 0, even = 0;
		for(int i = 0;i < n;i++){
			if(a[i] % 2 == 1){
				odds[odd++] = a[i];
			}else{
				evens[even++] = a[i];
			}
		}
		odds = Arrays.copyOf(odds, odd);
		evens = Arrays.copyOf(evens, even);
		
		if(odd % 2 == (K-p) % 2 && odd >= K-p && (odd-(K-p))/2 + (n-odd) >= p){
			out.println("YES");
			int[][] need = new int[K][];
			for(int i = 0;i < K-p;i++){
				need[i] = new int[]{0, 1};
			}
			int leftodd = odd-(K-p);
			int lefteven = n-odd;
			for(int i = K-p;i < K;i++){
				if(lefteven > 0){
					need[i] = new int[]{1, 0};
					lefteven--;
				}else{
					need[i] = new int[]{0, 2};
					leftodd -= 2;
				}
			}
			need[K-1][0] += lefteven;
			need[K-1][1] += leftodd;
			int op = 0, ep = 0;
			for(int i = 0;i < K;i++){
				out.print(need[i][0] + need[i][1]);
				for(int j = 0;j < need[i][0];j++){
					out.print(" "  + evens[ep++]);
				}
				for(int j = 0;j < need[i][1];j++){
					out.print(" "  + odds[op++]);
				}
				out.println();
			}
		}else{
			out.println("NO");
		}
	}

	void solve(InputStream is, PrintStream ps) {
		br = new BufferedReader(new InputStreamReader(is));
		out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(ps)));
		int n = ni();
		int k = ni();//k := # of all parts
		int p = ni();//p := # of parts with even sum
		int[] a = na(n);
		solve(n, k, p, a);
		out.close();
	}

	public static void main(String[] args) {
		new CF251Div2C().solve(System.in, System.out);
	}

	/*
	 *  common codes hereinafter
	 */

	static StringTokenizer st;
	static BufferedReader br;
	static PrintWriter out;

	String ns() {
		while (st == null || !st.hasMoreTokens())
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
				System.exit(1);
			}
		return st.nextToken();
	}

	int ni() {
		return Integer.parseInt(ns());
	}

	long nl() {
		return Long.parseLong(ns());
	}

	double nd() {
		return Double.parseDouble(ns());
	}

	int[] na(int n) {
		return na(n, 0);
	}

	int[] na(int n, int offset) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = ni() - offset;
		}
		return a;
	}

	int[][] na2(int n, int m) {
		return na2(n, m, 0);
	}

	int[][] na2(int n, int m, int offset) {
		int[][] a = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				a[i][j] = ni() - offset;
			}
		}
		return a;
	}

	boolean[][] nab(int n, int m) {
		boolean[][] a = new boolean[n][m];
		for (int i = 0; i < n; i++) {
			char[] cc = ns().toCharArray();
			for (int j = 0; j < cc.length; j++) {
				a[i][j] = cc[j] == '1';
			}
		}
		return a;
	}
}