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.*;
public class Main {
    static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }
    public static void main(String args[]) throws IOException {
        Scan input=new Scan();
        int n=input.scanInt();
        int k=input.scanInt();
        int p=input.scanInt();
        int arr[]=new int[n];
        for(int i=0;i<n;i++) {
            arr[i]=input.scanInt();
        }
        System.out.println(solve(n,k,p,arr));
    }
    public static StringBuilder solve(int n,int k,int p,int arr[]) {
        ArrayList<Integer> even=new ArrayList<>();
        ArrayList<Integer> odd=new ArrayList<>();
        for(int i=0;i<n;i++) {
            if(arr[i]%2==0) {
                even.add(arr[i]);
            }
            else {
                odd.add(arr[i]);
            }
        }
        StringBuilder ans=new StringBuilder("YES");
        ArrayList<Integer> tmp=new ArrayList<>();
        int e_rem=p;
        for(int i=0;i<even.size() && e_rem!=0;i++) {
            tmp=new ArrayList<>();
            if(e_rem==1) {
                for(int j=i;j<even.size();j++) {
                    tmp.add(even.get(j));
                }
                if(k-p==0) {
                    if(odd.size()%2==1) {
                        return new StringBuilder("NO");
                    }
                    for(int j=0;j<odd.size();j++) {
                        tmp.add(odd.get(j));
                    }
                }
                copy(ans,tmp);
                e_rem--;
                break;
            }
            else {
                tmp.add(even.get(i));
            }
            e_rem--;
            copy(ans,tmp);
        }
        int i=0;
        for(;i<odd.size() && e_rem!=0;i++) {
            tmp=new ArrayList<>();
            tmp.add(odd.get(i));
            i++;
            if(i==odd.size()) {
                break;
            }
            tmp.add(odd.get(i));
            if((k-p)==0 && e_rem==1) {
                for(int j=i+1;j<odd.size();j++) {
                    tmp.add(odd.get(j));
                }
                if(tmp.size()%2==1) {
                    return new StringBuilder("NO");
                }
                i=odd.size();
                copy(ans,tmp);
                e_rem--;
                break;
            }
            copy(ans,tmp);
            e_rem--;
        }
        
        int o_rem=k-p;
        for(;i<odd.size() && o_rem!=0;i++) {
            tmp=new ArrayList<>();
            if(o_rem==1) {
                if(p==0) {
                    for(int j=0;j<even.size();j++) {
                        tmp.add(even.get(j));
                    }
                }
                int count=0;
                for(int j=i;j<odd.size();j++) {
                    count++;
                    tmp.add(odd.get(j));
                }
                if(count%2==0) {
                    return new StringBuilder("NO");
                }
                copy(ans,tmp);
                o_rem--;
                break;
            }
            else {
                tmp.add(odd.get(i));
            }
            o_rem--;
            copy(ans,tmp);
        }
        if(e_rem!=0 || o_rem!=0) {
            return new StringBuilder("NO");
        }
        return ans;
    }
    public static void copy(StringBuilder ans,ArrayList<Integer> arrli) {
        ans.append("\n");
        ans.append(arrli.size()+" ");
        for(int i=0;i<arrli.size();i++) {
            ans.append(arrli.get(i)+" ");
        }
    }
}