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.io.*;
import java.math.*;
 
public class Main
{
    public static void process(int test_number)throws IOException
    {
        int n = ni(), k = ni(), reqEve = ni(), reqOdd = k - reqEve, cntEve = 0, cntOdd = 0;

        Queue<Integer> eveNum = new LinkedList<>() , oddNum = new LinkedList<>();
        ArrayList<Integer> oddList[] = new ArrayList[reqOdd], eveList[] = new ArrayList[reqEve];
        for(int i = 0; i < reqOdd; i++)
            oddList[i] = new ArrayList<>();
        for(int i = 0; i < reqEve; i++)
            eveList[i] = new ArrayList<>();

        for(int i = 1; i <= n; i++){
            int x = ni();
            if((x & 1) == 1){
                ++cntOdd;
                oddNum.add(x);
            } else{
                ++cntEve;
                eveNum.add(x);
            }
        }

        if(cntOdd < reqOdd)
            pn("NO");
        else{
            for(int i = 0; i < reqOdd; i++, --cntOdd){
                int x = oddNum.poll();
                oddList[i].add(x);
            }

            if((cntOdd & 1) == 1){
                pn("NO");
                return ;
            }

            int totalEve = 0;
            if(reqEve == 0){
                int idx = 0;
                while(!oddNum.isEmpty()){
                    int x = oddNum.poll(), y = oddNum.poll(); 
                    oddList[idx].add(x); 
                    oddList[idx].add(y); 
                    idx = (idx + 1) % reqOdd;
                }

                while(!eveNum.isEmpty()){
                    int x = eveNum.poll();
                    oddList[0].add(x);
                }
            } else{
                int idx = 0;
                while(!eveNum.isEmpty()){
                    int x = eveNum.poll(); ++totalEve;
                    eveList[idx].add(x);
                    idx = (idx + 1) % reqEve;
                }

                while(!oddNum.isEmpty()){
                    int x = oddNum.poll(), y = oddNum.poll(); ++totalEve;
                    eveList[idx].add(x); 
                    eveList[idx].add(y); 
                    idx = (idx + 1) % reqEve;
                }
            }
            

            if(totalEve < reqEve)
                pn("NO");
            else{
                p("YES\n");
                for(int i = 0; i < reqOdd; i++){
                    p(oddList[i].size() + " ");
                    for(int x : oddList[i])
                        p(x + " ");
                    p('\n');
                }

                for(int i = 0; i < reqEve; i++){
                    p(eveList[i].size() + " ");
                    for(int x : eveList[i])
                        p(x + " ");
                    p('\n');
                }
            }
        }
    }
    
    static final int oo = (int) 1e9 + 100;
    static final long mod = (long)1e9+7l;
    static boolean DEBUG = true;
    static FastReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc = new FastReader();
 
        long s = System.currentTimeMillis();
        int t = 1;
        // t = ni();
        for(int i = 1; i <= t; i++)
            process(i);
 
        out.flush();
        System.err.println(System.currentTimeMillis()-s+"ms");
    }

    static void trace(Object... o){ if(!DEBUG) return; System.err.println(Arrays.deepToString(o)); };    
    static void pn(Object o){ out.println(o); }
    static void p(Object o){ out.print(o); }
    static int ni()throws IOException{ return Integer.parseInt(sc.next()); }
    static long nl()throws IOException{ return Long.parseLong(sc.next()); }
    static double nd()throws IOException{ return Double.parseDouble(sc.next()); }
    static String nln()throws IOException{ return sc.nextLine(); }
    static long gcd(long a, long b){ return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b){ return (b==0)?a:gcd(b,a%b); }
    
    static class FastReader{ 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader(){ 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next(){ 
            while (st == null || !st.hasMoreElements()){ 
                try{ st = new StringTokenizer(br.readLine()); } catch (IOException  e){ e.printStackTrace(); } 
            } 
            return st.nextToken(); 
        } 
  
        String nextLine(){ 
            String str = ""; 
            try{ str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } 
            return str; 
        } 
    } 
}