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.util.*;
import java.math.*;
import java.io.*;
public class C {
    public static long time = 0;
    public static void main(String[] args) throws Exception {
        time = System.currentTimeMillis();
        
        IN = System.in;
        OUT = System.out;
        in = new BufferedReader(new InputStreamReader(IN));
        out = new PrintWriter(OUT, FLUSH);
        solveOne();
        out.flush();
    }
    
    public static void solveOne() throws Exception {
        int n = nextInt();
        int k = nextInt();
        int p = nextInt();
        int evenPart = p;
        int oddPart = k - p;
        ArrayDeque<Integer> even = new ArrayDeque<>();
        ArrayDeque<Integer> odd = new ArrayDeque<>();
        for (int e: nextIntArray(n)){
            if (e % 2 == 0){
                even.add(e);
            }
            else odd.add(e);
        }
        if (odd.size() < oddPart){
            pn("NO");
        }
        else if ((odd.size() - oddPart) %2 != 0){
            pn("NO");
        }
        else {
            int oddPair = (odd.size() - oddPart) / 2;
            int totalHaveEven = even.size() + oddPair;
//          px("hit", totalEven);
            if (totalHaveEven < evenPart){
                pn("NO");
            }
            else {
                pn("YES");
                ArrayList<Integer>[] evenPartList = new ArrayList[evenPart];
                for (int i = 0 ; i < evenPartList.length; i++){
                    evenPartList[i] = new ArrayList<>();
                    if (odd.size() - oddPart > 0){
                        evenPartList[i].add(odd.poll());
                        evenPartList[i].add(odd.poll());
                    }
                    else {
                        evenPartList[i].add(even.poll());
                    }
                }
                if (evenPart != 0){
                    for (;;){
                        if (odd.size() - oddPart > 0){
                            evenPartList[0].add(odd.poll());
                            evenPartList[0].add(odd.poll());
                        }
                        else if (even.size() > 0){
                            evenPartList[0].add(even.poll());
                        }
                        else break;
                    }
                }
                
                for (int i =0 ; i < evenPartList.length; i++){
                    p(evenPartList[i].size() + " ");
                    for (int e: evenPartList[i]){
                        p(e + " ");
                    }
                    pn();
                }
                
                for (int i = 0 ; i <oddPart; i++){
                    int cur = odd.poll();
                    if (i == 0 && evenPart == 0){
                        ArrayList<Integer> fin = new ArrayList();
                        for (;;){
                            if (odd.size() - oddPart > 0){
                                fin.add(odd.poll());
                                fin.add(odd.poll());
                            }
                            else if (even.size() > 0){
                                fin.add(even.poll());
                            }
                            else break;
                        }
                        fin.add(cur);
                        p(fin.size() + " ");
                        for (int e: fin){
                            p(e + " ");
                        }
                        pn();
                    }
                    else {
                        pn(1 + " " + cur);
                        
                    }
                }
            }
            
        }
        
        
    }
    
    public static void solveTwo() throws Exception {
        
    }
    
    public static void solveThree() throws Exception {
        
    }
    
    public static BufferedReader in;
    public static StringTokenizer st;
    public static InputStream IN;
    public static OutputStream OUT;
    public static String nextString() throws Exception {
        for (;st == null || !st.hasMoreTokens();){
            String k1 = in.readLine();
            if (k1 == null) return null;
            st = new StringTokenizer(k1);
        }
        return st.nextToken();
    }
    public static int nextInt () throws Exception {
        return Integer.parseInt(nextString());
    }
    public static long nextLong() throws Exception{
        return Long.parseLong(nextString());
    }
    public static double nextDouble() throws Exception{
        return Double.parseDouble(nextString());
    }
    private static int[] nextIntArray(int n1) throws Exception {
        int[] l1 = new int[n1];
        for (int i = 0 ;i < n1; i++){
            l1[i] = nextInt();
        }
        return l1;
    }
    private static long[] nextLongArray(int n1) throws Exception {
        long[] l1 = new long[n1];
        for (int i = 0 ;i < n1; i++){
            l1[i] = nextLong();
        }
        return l1;
    }
    private static int[][] nextIntGrid(int x, int y) throws Exception {
        int[][] l1 = new int[x][y];
        for (int i =0; i < x; i++){
            for (int j = 0; j < y; j++){
                l1[i][j] = nextInt();
            }
        }
        return l1;
    }
    public static void px(Object ... l1){
        System.out.println(Arrays.deepToString(l1));
    }
    public static boolean FLUSH = false;
    public static PrintWriter out;
    public static void p(Object ... l1){
        for (int i = 0; i < l1.length; i++){
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
    }
    public static void pn(Object ... l1){
        for (int i = 0; i < l1.length; i++){
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
        out.println();
    }
    
    public static void pn(Collection l1){
        boolean first = true;
        for (Object e: l1){
            if (first) first = false;
            else out.print(' ');
            out.print(e.toString());
        }
        out.println();
    }
    
    private static BigInteger bi(long n1){
        return BigInteger.valueOf(n1);
    }
    
    private static double usedTime(){
        return (System.currentTimeMillis()-time)*0.001;
    }
    
    
    
}