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.math.BigInteger;
import java.util.*;


 public class Main {
	public static InputReader in;
    public static PrintWriter pw;



	public static void main(String args[]) {
		new Thread(null, new Runnable() {
            public void run() {
                try{
                    solve();
                }
                catch(Exception e){
                    e.printStackTrace();
                }
            }
        }, "1", 1 << 26).start();
    }
	static TreeSet<Integer> set;
	static ArrayList<Pair> g[];
	static boolean visited[];
	static long edje=0;
    static boolean vis[];
	static int parent[];
	static int col[];
	static boolean[] vis1;
	static int Ans=0;
	static int min=Integer.MAX_VALUE;
	static int val[];
	static int degree[];
	static int a[];
	static int f[];
	static  long total=0;
	static HashSet<String> s;
	static int distance[];
	public static void solve(){
	
		 in = new InputReader(System.in);
		 pw = new PrintWriter(System.out);
         int n=in.nextInt();
         int k=in.nextInt();
         int even=in.nextInt();
         int odd=k-even;
         int a[]=in.nextIntArray(n);
         int e=0;
         int o=0;
         Queue<Integer> QO=new LinkedList<Integer>();
         Queue<Integer> QE=new LinkedList<Integer>();
         for(int i=0;i<n;i++)
         {
        	 if(a[i]%2==0)
        	 {
        		 e++;
        		 QE.add(a[i]);
        	 }
        	 else{
        		 QO.add(a[i]);
        		 o++;
        	 }
         }
         ArrayList<Integer> es[]=new ArrayList[even];
         for(int i=0;i<even;i++)
        	 es[i]=new ArrayList<Integer>();
         ArrayList<Integer> os[]=new ArrayList[odd];
         for(int i=0;i<odd;i++)
        	 os[i]=new ArrayList<Integer>();
         int tt=even;
         int p=0;
         while(!QE.isEmpty()&&p<even)
         {
        	 if(p<even)
        	 es[p++].add(QE.poll());
         }
         if(p<even)
         {
        	 while(QO.size()>=2&&p<even)
        	 {
        		 int o1=QO.poll();
        		 int o2=QO.poll();
        		 es[p].add(o1);
        		 es[p].add(o2);
        		 p++;
        	 }
        	 if(p<even)
        	 {
        		 System.out.println("NO");
        		 System.exit(0);
        	 }
         }
         int q=0;
         while(!QO.isEmpty()&&q<odd)
         {
        	 if(q<odd)
        	 {
        	 os[q++].add(QO.poll());
        	 }
         }
     // System.out.println(QO);
         
         //System.out.println("---");
         if(q<odd)
         {
        	/* while(!QE.isEmpty()&&q<odd)
        	 {
        		 int o1=QE.poll();
        		 os[q].add(o1);
        		 q++;
        	 }*/
        	 if(q<odd)
        	 {
        		 System.out.println("NO");
        		 System.exit(0);
        	 }
         }
         while(!QE.isEmpty())
         {
        	 int x=QE.poll();
        	 if(even>0)
        	 {
        		 es[0].add(x);
        	 }
        	 else
        		 os[0].add(x);
         }
         //System.out.println(QO);
         while(QO.size()>=2)
         {
        	 if(even>0)
        	 {
        		 int o1=QO.poll();
        		 int o2=QO.poll();
        		 es[0].add(o1);
        		 es[0].add(o2);
        	 }
        	 else
        		 break;
         }
         if(QO.size()%2!=0)
         {
        	 System.out.println("NO");
        	 System.exit(0);
         }
        // System.out.println(QO);
         while(!QO.isEmpty())
         {
        	 int o1=QO.poll();
    		 int o2=QO.poll();
    		 os[0].add(o1);
    		 os[0].add(o2);
         }
         System.out.println("YES");
         StringBuilder ans1=new StringBuilder();
         for(int i=0;i<even;i++)
         {
        	ans1.append(es[i].size()+" ");
        	 for(int j=0;j<es[i].size();j++)
        		 ans1.append(es[i].get(j)+" ");
        	ans1.append("\n");
         }
         StringBuilder ans2=new StringBuilder();
         for(int i=0;i<odd;i++)
         {
        	ans2.append(os[i].size()+" ");
        	 for(int j=0;j<os[i].size();j++)
        		ans2.append(os[i].get(j)+" ");
        	ans2.append("\n");
         }
         System.out.print(ans1);
         System.out.println(ans2);
	}

	/*public static void dfs(int curr)
	{
		vis[curr]=true;
		int trees=0;
		for(int x:g[curr])
		{
			if(!vis[x]&&x!=1)
			{
			trees++;
			if(!s.contains(curr+" "+x))
				total+=cost[curr][x];
			dfs(x);
			}
	    }
		if(trees==0)
		{
			if(!s.contains(curr+" "+1))
				total+=cost[1][curr];
		}
	}
	public static void dfs1(int curr,int parent)
	{
	val[curr]=a[curr];
	for(int x:g[curr])
	{
	       if(x!=parent)
	       {
	    	   dfs1(x,curr);
	    	   val[curr]+=val[x];
	      }
	
	}
	}
	public static void dfs2(int curr,int parent)
	{
		f[curr]=val[curr];
		for(int x:g[curr])
		{
			if(x!=parent)
			{
				dfs2(x,curr);
				f[curr]+=f[x];
			}
		}
	}
	
	
	 
/*    public static void dfs2(int curr)
    {
    if(st[col[curr]].isEmpty())
    {
    ans[curr]=-1;	
    }
    else
    {
    	ans[curr]=st[col[curr]].peek();
    }
    st[col[curr]].push(curr);
    for(int x:g[curr])
    {
    	dfs2(x);
    }
    st[col[curr]].pop();
    	
    }
    
  
	public static void dfs1(int curr)
	{
		visited[curr]=true;
		for(int next:g[curr])
		{
			edje++;
			if(!visited[next])
				dfs1(next);
		}
	}
	
	public static void dfs(int curr,int prev)
		{
		val[curr]=1;
			for(int x:g[curr])
			{
				if(x!=prev)
				{
		            dfs(x,curr);
		            val[curr]+=val[x];
					
			    }
			}
		}*/
	
		public static long power(long a,long b)
		{
			long result=1;
			while(b>0)
			{
				if(b%2==1)
					result*=a;
				a=a*a;
				b/=2;
			}
			return result;
		}
				public static long pow(long n,long p,long m)
	{
		 long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    if(result>=m)
		    result%=m;
		    p >>=1;
		    n*=n;
		    if(n>=m)
		    n%=m;
		}
		return result;
	}
	static class Pair implements Comparable<Pair>{
	int ind;
		int val;
		Pair(int mr,int i){
	     	ind=mr;
			val=i;
			
		}
		@Override
		public int compareTo(Pair o) {
		//	if(o.val<this.val)
		
			return 1;
			
			//else 
				//return -1;
			
			}
		
	}
	public static long gcd(long a, long b) {
		  if (b == 0) return a;
		  return gcd(b, a%b);
		}
	static class InputReader {
 
		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
 
		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public   int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}