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.*;
import java.util.*;

// :%s/C439/"name"/
// if (debug) 

public class C439 {
	public static void main(String[] args) { new C439(); }
	FS in = new FS();
	PrintWriter out = new PrintWriter(System.out);

	int t;
	int n, k, p;
	int[] a;
	ArrayList<Integer>[] grpE, grpO;

	boolean debug = !true, multi = !true;

	C439() {
		if (multi) t = in.nextInt();
		do {
			if (multi) if (z(t--)) break;

			n = in.nextInt();
			k = in.nextInt();
			p = in.nextInt();
			a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = in.nextInt();

			grpE = new ArrayList[p];
			grpO = new ArrayList[k - p];
			for (int i = 0; i < p; i++)
				grpE[i] = new ArrayList<>();
			for (int i = 0; i < k - p; i++)
				grpO[i] = new ArrayList<>();

			int[] e = new int[n + 1];
			int[] o = new int[n + 1];
			for (int i = 0; i < n; i++) {
				if (z(a[i] & 1))
					e[++e[0]] = a[i];
				else
					o[++o[0]] = a[i];
			}

			int ptrE = 0, ptrO = 0;
			while (ptrE < p && !z(e[0]))
				grpE[ptrE++].add(e[e[0]--]);
			while (ptrO < k - p && !z(o[0]))
				grpO[ptrO++].add(o[o[0]--]);

			if (ptrO != k - p || !z(o[0] & 1)) {
				out.println("NO");
				break;
			}

			// if we got enough even groups, throw the rest into the first one
			// all the below will cause RTE if p == 0
			while (!z(e[0])) {
				if (!z(p))
					grpE[0].add(e[e[0]--]);
				else
					grpO[0].add(e[e[0]--]);
			}
			// othewise the even groups must be made of pairs of odds
			while (ptrE < p && !z(o[0])) {
				grpE[ptrE].add(o[o[0]--]);
				grpE[ptrE].add(o[o[0]--]);
				ptrE++;
			}
			// if this still didn't work then we're doomed
			if (ptrE != p) {	
				out.println("NO");
				break;
			}
			// if we have enough even/odd groups
			// just pour pairs of odds into the first even
			while (!z(o[0])) {
				if (!z(p)) {
					grpE[0].add(o[o[0]--]);
					grpE[0].add(o[o[0]--]);
				}
				else {
					grpO[0].add(o[o[0]--]);
					grpO[0].add(o[o[0]--]);
				}
			}
			
			out.println("YES");
			if (!z(p))
				for (ArrayList<Integer> g : grpE) {
					out.print(g.size() + " ");
					for (int i : g)
						out.print(i + " ");
					out.println();
				}
			if (!z(k - p))
				for (ArrayList<Integer> g : grpO) {
					out.print(g.size() + " ");
					for (int i : g)
						out.print(i + " ");
					out.println();
				}
				
		} while (debug || multi);
		out.close();
	}

	

	int min(int a, int b) { if (a < b) return a; return b; }	
	int max(int a, int b) { if (a > b) return a; return b; }	
	long min(long a, long b) { if (a < b) return a; return b; }	
	long max(long a, long b) { if (a > b) return a; return b; }	

	boolean z(int x) { if (x == 0) return true; return false; }	
	boolean z(long x) { if (x == 0) return true; return false; }	

	void sort(int[] arr) {
		int sz = arr.length, j;
		Random r = new Random();
		for (int i = 0; i < sz; i++) {
			j = r.nextInt(sz);
			arr[i] = arr[j]^(arr[i]^(arr[j] = arr[i]));
		} Arrays.sort(arr);
	}

	class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens()) {
				try { st = new StringTokenizer(br.readLine()); }
				catch (Exception e) {}
			} return st.nextToken();
		}
		int nextInt() { return Integer.parseInt(next()); }
		long nextLong() { return Long.parseLong(next()); }
		double nextDouble() { return Double.parseDouble(next()); }
	}
}