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.*;

public class Solution {

    public static void solve(InputReader in, PrintWriter out, DebugWriter debug) throws IOException {
        int n = in.nextInt();
        int k = in.nextInt();
        int p = in.nextInt();
        int[] a = in.nextIntArray(n);
        boolean[] use = new boolean[n];

        ArrayList<ArrayList<Integer>> evenSum = new ArrayList<>();
        ArrayList<ArrayList<Integer>> oddSum = new ArrayList<>();

        if (p != 0) {
            int evenNow = 0;
            for (int i = 0; i < n; i++) {
                if (a[i] % 2 == 0) {
                    ArrayList<Integer> newList = new ArrayList<>();
                    newList.add(i);
                    use[i] = true;
                    evenSum.add(newList);

                    evenNow++;
                    if (evenNow == p) break;
                }
            }

            if (evenNow != p) {
                ArrayList<Integer> lastList = null;
                for (int i = 0; i < n; i++) {
                    if (a[i] % 2 == 1) {
                        if (lastList == null) lastList = new ArrayList<>();
                        lastList.add(i);
                        use[i] = true;

                        if (lastList.size() == 2) {
                            evenSum.add(lastList);
                            lastList = null;

                            evenNow++;
                            if (evenNow == p) break;
                        }
                    }
                }
            }

            if (evenNow != p) {
                out.print("NO");
                return;
            }
        }

        if (k-p != 0) {
            int oddNow = 0;
            for (int i = 0; i < n; i++) {
                if (a[i] % 2 == 1 && !use[i]) {
                    ArrayList<Integer> newList = new ArrayList<>();
                    newList.add(i);
                    use[i] = true;
                    oddSum.add(newList);

                    oddNow++;
                    if (oddNow == k - p) break;
                }
            }

            if (oddNow != k - p) {
                out.print("NO");
                return;
            }
        }

        ArrayList<Integer> other = (oddSum.size() != 0)? oddSum.get(0) : evenSum.get(0);
        boolean changeType = false;
        for (int i=0; i<n; i++){
            if (!use[i]){
                other.add(i);
                use[i] = true;

                if (a[i] % 2 == 1) changeType = !changeType;
            }
        }

        if (changeType){
            out.print("NO");
            return;
        }

        out.println("YES");
        print(evenSum, a, out);
        print(oddSum, a, out);
    }

    public static void print(ArrayList<ArrayList<Integer>> allLists, int[] a, PrintWriter out){
        for (ArrayList<Integer> list : allLists){
            out.print(list.size() + " ");
            for (int i : list) out.print(a[i] + " ");
            out.println();
        }
    }

    public static void main(String[] args) throws IOException{
        InputReader in;
        PrintWriter out;
        DebugWriter debug;

        if (args.length > 0 && args[0].equals("file")) {
            in = new InputReader(new BufferedReader(new FileReader("input.txt")));
            out = new PrintWriter(new FileWriter("output.txt"));
            debug = new DebugWriter(true);

            int sampleNumber = 1;
            do {
                String nextSample = "Sample #" + sampleNumber++ + ": ";
                out.println(nextSample);
                debug.println(nextSample);

                solve(in, out, debug);

                out.println("");
                debug.println("");
            } while (in.reader.readLine() != null);
        } else {
            in = new InputReader(new BufferedReader(new InputStreamReader(System.in)));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            debug = new DebugWriter(false);

            solve(in, out, debug);
        }

        in.reader.close();
        out.close();
    }

    public static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(BufferedReader reader) {
            this.reader = reader;
            tokenizer = null;
        }

        public String next() throws IOException{
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }

            return tokenizer.nextToken();
        }

        public int nextInt() throws IOException{
            return Integer.parseInt(next());
        }

        public int[] nextIntArray(int n) throws IOException{
            int[] array = new int[n];
            for (int i=0; i<n; i++){
                array[i] = nextInt();
            }

            return array;
        }
    }

    public static class DebugWriter {
        public boolean enable;

        public DebugWriter(boolean enable){
            this.enable = enable;
        }

        public void print(Object o){
            if (enable) System.out.print(o);
        }

        public void println(Object o){
            if (enable) System.out.println(o);
        }
    }

}