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.*;
import java.lang.*;
import java.math.BigInteger;
import java.util.Map.Entry;
import java.util.logging.Level;
import java.util.logging.Logger;


public class Main
{
    static StringTokenizer st=new StringTokenizer("");
    static BufferedReader br;
    
    ///////////////////////////////////////////////////////////////////////////////////
    
    
    public static void main(String args[]) throws FileNotFoundException, IOException, Exception
    {
        //Scanner class
        //Scanner in =new Scanner(new FileReader("input.txt"));
        //Scanner in=new Scanner(System.in);
        
        //PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
        //br=new BufferedReader(new FileReader("input.txt"));
        
        br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out=new PrintWriter(System.out);
        
        //StringTokenizer st;//=nedsw StringTokenizer(br.readLine());
        //////////////////////////////////////////////////////////////////////////////////////
        
        int n=ni(),k=ni(),p=ni();
        int arr[]=new int[n];
        int odd=0,even=0;
        StringBuffer res=new StringBuffer("");
        for(int i=0;i<n;i++)
        {
            arr[i]=ni();
            if(arr[i]%2==0) even++;
            else odd++;
        }
        int temp=0;
        if(even<p)
            temp=2*(p-even);
        if(odd-temp<(k-p))
        {
            out.print("NO");
            out.close();
            return ;
        }
        res.append("YES\n");
        //out.println("YES");
        boolean used[]=new boolean[n];
        int cnt=0;
        int i=0;
        for(int j=1;j<p;j++)
        {
            loop2:for(;i<n;i++)
            {
                if(arr[i]%2==0 && !used[i])
                {
                    used[i]=true;
                    res.append("1 "+arr[i]+"\n");
                    //out.println("1 "+arr[i]);
                    cnt++;
                    break loop2;
                }
            }
        }
        if(cnt<p-1 || even-cnt==0 ||k==p)
        {
            i=0;
            int j=(k-p==0)?1:0;
            boolean yes=(j==1)?true:false;
            for(;j<(p-cnt);j++)
            {
                int k1=0;
                res.append("2 ");
                //out.print("2 ");
                loop2:for(;i<n;i++)
                {
                    if(!used[i])
                    {
                        used[i]=true;
                        k1++;
                        res.append(arr[i]+" ");
                        //out.print(arr[i]+" ");
                        if(k1==2) break loop2;
                    }
                }
                res.append("\n");
                //out.println();
            }
            int n1=0;
            int o1=0;
            StringBuffer a1=new StringBuffer("");
            if(yes)
            {
                for(i=0;i<n;i++)
                {
                    if(!used[i])
                    {
                        used[i]=true;
                        a1.append(arr[i]+" ");
                        n1++;
                        if(arr[i]%2==1)o1++;
                    }
                }
                if(o1%2==1)
                {
                    out.print("NO");
                    out.close();
                    return ;
                }
                else 
                {
                    res.append(n1+" "+a1+"\n");
                }
            }
        }
        else if(p>0)
        {
            int k1=0;
            StringBuilder a1=new StringBuilder("");
            i=0;
            for(;i<n;i++)
            {
                if(!used[i] && arr[i]%2==0)
                {
                    used[i]=true;
                    k1++;
                    a1.append(arr[i]+" ");
                }
            }
            if(k1>0)
            res.append(k1+" "+a1+"\n");
            //out.print(k1+" ");
            //out.println(a1);
            //out.println("k1 "+k1);
        }
        i=0;
        for(int j=1;j<k-p;j++)
        {
            loop2:for(;i<n;i++)
            {
                if(!used[i])
                {
                    used[i]=true;
                    res.append("1 "+arr[i]+"\n");
                    //out.println("1 "+arr[i]);
                    break loop2;
                }
            }
        }
        StringBuffer a1=new StringBuffer("");
        int c=0;
        int e=0;
        for(;i<n;i++)
        {
            if(!used[i])
            {
                used[i]=true;
                a1.append(arr[i]+" ");
                c++;
                if(arr[i]%2!=0) e++;
            }
        }
        if(c>0)
        res.append(c+" "+a1+"\n");
        //out.println(c+" "+a1);
        if(e%2==0 && c!=0)
        {
            //out.println(c);
            out.print("NO");
        }
        else out.print(res);
        //////////////////////////////////////////////////////////////////////////////////////
	out.close();
    }
    
    
    
    
    ///////////////////////////////////////////////////////////////////////////////
    
    private static long gcd(long a,long b)
    {
        if(b==0)
            return a;
        return gcd(b,a%b);
    }
    private static class pair implements Comparable<pair>
    {
        int first;
        int second;
        pair()
        {
            first=0;
            second=0;
        }
        pair(int f,int s)
        {
            first=f;
            second=s;
        }

        public int compareTo(pair o)
        {
            if(second >  o.second)
                return 1;
            else if(second < o.second)
                return -1;
            else
                return 0;
        }
    }
    
    public static Integer ni() throws Exception
    {
        if(!st.hasMoreTokens())
            st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    public static BigInteger nb()throws Exception
    {
        if(!st.hasMoreElements())
            st=new StringTokenizer(br.readLine());
        return BigInteger.valueOf(Long.parseLong(st.nextToken()));
    }
    public static Long nl() throws Exception
    {
        if(!st.hasMoreTokens())
            st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    public static Double nd()throws Exception
    {
        if(!st.hasMoreElements())
            st=new StringTokenizer(br.readLine());
        return Double.parseDouble(st.nextToken());
    }
    public static String ns()throws Exception
    {
        if(!st.hasMoreElements())
            st=new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}