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.util.regex.* ;
import java.text.* ;
import java.math.* ;

public class Main {
	public static void main( String[] args ) {
		InputStream isObj ;
		OutputStream osObj ;
		InputReader irObj ;
		PrintWriter pwObj ;
		String inputFileName , outputFileName ;
		File fObj1 , fObj2 ;
		int T , ind ;
		boolean hasMoreInput , hasTestCases ;
		ProblemSolver psObj ;
		//only variable to be changed here is hasTestCases and osObj(optional for file output)
		hasTestCases = ProblemSolver.HAS_TEST_CASES ;
		isObj = System.in ;
		osObj = System.out ;
		inputFileName = ProblemSolver.INPUT_FILE_NAME ;
		outputFileName = ProblemSolver.OUTPUT_FILE_NAME ;
		try {
			fObj1 = new File( System.getProperty( "user.dir" ).toString() + "\\" + inputFileName ) ;
			fObj2 = new File( System.getProperty( "user.dir" ).toString() + "\\" + outputFileName ) ;
			if( fObj1.exists() == false ) {
				fObj1 = new File( System.getProperty( "user.dir" ).toString() + "\\src\\" + inputFileName ) ;
				fObj2 = new File( System.getProperty( "user.dir" ).toString() + "\\src\\" + outputFileName ) ;
			}
			isObj = new FileInputStream( fObj1 ) ;
			if( ProblemSolver.DO_OUTPUT_TO_FILE == true ) {
				osObj = new FileOutputStream( fObj2 ) ;
			}
		}
		catch( Exception ex ) {
			ex.printStackTrace() ;
			isObj = System.in ;
			osObj = System.out ;
		}
		irObj = new InputReader( isObj ) ;
		pwObj = new PrintWriter( osObj ) ;
		try {
			psObj = new ProblemSolver() ;
			if( hasTestCases == true ) {
				//for input with test cases
				T = irObj.nextInt() ;
				for( ind = 1 ; ind <= T ; ind++ ) {        	
					psObj.clearPerCase() ;
					psObj.getInput( irObj ) ;
					psObj.solveCase( pwObj ) ;
				}
			}
			else {
				//for end of file input
				for( ind = 1 ; ; ind++ ) {        	
					psObj.clearPerCase() ;
					hasMoreInput = psObj.getInput( irObj ) ;
					if( hasMoreInput == false ) {
						break ;
					}
					psObj.solveCase( pwObj ) ;
				}
			}
			pwObj.flush() ;
			isObj.close() ;
			osObj.close() ;
		}
		catch( Exception ex ) {
			ex.printStackTrace() ;
			throw new RuntimeException( ex ) ;
		}
		finally {
			pwObj.close() ;
		}
	}
}

class ProblemSolver {
	public static final boolean HAS_TEST_CASES = false ;
	public static final String INPUT_FILE_NAME = "test.in" ;
	public static final String OUTPUT_FILE_NAME = "out.txt" ;
	public static final boolean DO_OUTPUT_TO_FILE = false ;
	
	public void solveCase( PrintWriter pwObj ) {
		int i , j , a , b , c , d , e , u , v , sz , left ;
		boolean res ;
		res = true ;
		this.cnt1 = 0 ;
		this.cnt2 = 0 ;
		for( i = 0 ; i < this.n ; i++ ) {
			c = this.arr[ i ] % 2 ;
			if( c == 0 ) {
				this.err[ this.cnt1++ ] = this.arr[ i ] ;
			}
			else {
				this.frr[ this.cnt2++ ] = this.arr[ i ] ;
			}
		}
		u = 0 ;
		v = 0 ;
		for( i = 0 ; i < this.p ; i++ ) {
			if( u < this.cnt1 ) {
				d = this.err[ u ] ;
				this.adj_list[ i ].add( d ) ;
				u++ ;
			}
			else if( v + 1 < this.cnt2 ) {
				d = this.frr[ v ] ;
				v++ ;
				this.adj_list[ i ].add( d ) ;
				d = this.frr[ v ] ;
				v++ ;
				this.adj_list[ i ].add( d ) ;
			}
			else {
				res = false ;
				break ;
			}
		}
		for( i = this.p ; i < this.k ; i++ ) {
			if( v < this.cnt2 ) {
				d = this.frr[ v ] ;
				this.adj_list[ i ].add( d ) ;
				v++ ;
			}
			else {
				res = false ;
				break ;
			}
		}
		if( u < this.cnt1 ) {
			for( i = u ; i < this.cnt1 ; i++ ) {
				this.adj_list[ 0 ].add( this.err[ i ] ) ;
			}
		}
		if( v < this.cnt2 ) {
			left = ( this.cnt2 - v ) ;
			if( left % 2 == 0 ) {
				for( i = v ; i < this.cnt2 ; i++ ) {
					this.adj_list[ 0 ].add( this.frr[ i ] ) ;
				}
			}
			else {
				res = false ;
			}
		}
		if( res == true ) {
			pwObj.println( "YES" ) ;
			for( i = 0 ; i < this.k ; i++ ) {
				sz = this.adj_list[ i ].size() ;
				pwObj.print( sz ) ;
				for( j = 0 ; j < sz ; j++ ) {
					pwObj.print( " " + this.adj_list[ i ].get( j ) ) ;
				}
				pwObj.println( "" ) ;
			}
		}
		else {
			pwObj.println( "NO" ) ;
		}
	}
	
	private void init() {
		//default values
		this.lim1 = 100010 ;
		this.lim2 = 110 ;
		this.cc = 1 ;
		this.ind = 0 ;
		this.declareArrays() ;
		this.fillAllArrays() ;
	}
	
	public boolean getInput( InputReader irObj ) {
		int i ;
		try {
			this.n = irObj.nextInt() ;
		}
		catch( Exception ex ) {
			return false ;
		}
		this.k = irObj.nextInt() ;
		this.p = irObj.nextInt() ;
		for( i = 0 ; i < this.n ; i++ ) {
			this.arr[ i ] = irObj.nextInt() ;			
		}
		return true ;
	}
	
	private int lim1 , lim2 , cn , ind , cc , n , k , p , cnt1 , cnt2 ; 
	private String[] srr ;
	private int[] arr , brr , crr , drr , err , frr ;
	private Node[] nrr ;
	private long[] lrr ;
	private int[][] memo , done ;
	private ArrayList< Integer >[] adj_list ;
	
	public void clearPerCase() {
		int i ;
		for( i = 0 ; i < this.lim1 ; i++ ) {
			this.adj_list[ i ].clear() ;
		}
		this.incrementInd() ;
		this.incrementCc() ;
		this.n = 0 ;
		this.cn = 0 ;
		Arrays.fill( this.drr , 0 ) ;
		Arrays.fill( this.crr , 0 ) ;
	}
	
	private void declareArrays() {
		//array declarations
		this.arr = new int[ this.lim1 ] ;
		this.brr = new int[ this.lim1 ] ;
		this.crr = new int[ this.lim1 ] ;
		this.drr = new int[ this.lim1 ] ;
		this.err = new int[ this.lim1 ] ;
		this.frr = new int[ this.lim1 ] ;
		this.lrr = new long[ this.lim1 ] ;
		this.srr = new String[ this.lim1 ] ;
		this.nrr = new Node[ this.lim1 ] ;
		this.memo = new int[ this.lim2 ][ this.lim2 ] ;
		this.done = new int[ this.lim2 ][ this.lim2 ] ;
		this.adj_list = new ArrayList[ this.lim1 ] ;
	}
	
	private void fillAllArrays() {
		int i ;
		//array initiations
		Arrays.fill( this.arr , 0 ) ;
		Arrays.fill( this.brr , 0 ) ;
		Arrays.fill( this.drr , 0 ) ;
		Arrays.fill( this.crr , 0 ) ;
		Arrays.fill( this.err , 0 ) ;
		Arrays.fill( this.frr , 0 ) ;
		Arrays.fill( this.lrr , 0 ) ;
		for( int zrr[] : this.memo ) {
			Arrays.fill( zrr , -1 ) ;
		}
		for( int zrr[] : this.done ) {
			Arrays.fill( zrr , 0 ) ;
		}
		for( i = 0 ; i < this.lim1 ; i++ ) {
			this.srr[ i ] = new String( "" ) ;
			this.nrr[ i ] = new Node( Integer.MIN_VALUE , Integer.MIN_VALUE ) ;
			this.adj_list[ i ] = new ArrayList< Integer >() ;
		}
	}
	
	private void incrementInd() {
		this.ind++ ;
	}
	
	public void setCn( int c ) {
		this.cn = c ;  
	}
	
	public void incrementCn() {
		this.cn++ ;
	}
	
	public void incrementCc() {
		this.cc++ ;
	}
	
	public int getCn() {
		return this.cn ;
	}
	
	public ProblemSolver() {
		this.init() ;
	}
}

class Node implements Comparable< Node > {
	private int v , f ;
	
	private Node() {
	}
	
	public Node( int vParam , int fParam ) {
		this.v = vParam ;
		this.f = fParam ;
	}
	
	public void setV( int vParam ) {
		this.v = vParam ;
	}
	
	public void setF( int fParam ) {
		this.f = fParam ;
	}
	
	public int getV() {
		return this.v ;
	}
	
	public int getF() {
		return this.f ;
	}
	
	public int compareTo( Node nParam ) {
		return this.getV() - nParam.getV() ;
	}
}

class InputReader {
	private BufferedReader reader ;
	private StringTokenizer tokenizer ;

	public InputReader( InputStream stream ) {
		this.reader = new BufferedReader( new InputStreamReader( stream ) ) ;
		this.tokenizer = null ;
	}

	private String next( int fl ) {
		while( this.tokenizer == null || ! this.tokenizer.hasMoreTokens() ) {
			try {                
				this.tokenizer = new StringTokenizer( this.reader.readLine() ) ;
			}
			catch( IOException e ) {
				throw new RuntimeException( e ) ;
			}
		}
		String s ;
		s = "" ;
		if( fl == 1 ) {
			s = this.tokenizer.nextToken() ; 
		}
		return s ;
	}

	public String nextLine() {
		this.next( 0 ) ;
		int fl ;
		String line ;
		line = "" ;
		fl = 0 ;
		if( this.tokenizer != null ) {
			while( this.tokenizer.hasMoreTokens() ) {
				if( fl == 1 ) {
					line += " " ;
				}
				fl = 1 ;
				line += this.tokenizer.nextToken() ;
			}
		}
		return line ;
	}

	public int nextInt() {
		return Integer.parseInt( this.next( 1 ) ) ;
	}

	public long nextLong() {
		return Long.parseLong( this.next( 1 ) ) ;
	}

	public double nextDouble() {
		return Double.parseDouble( this.next( 1 ) ) ;
	}

	public String nextString() {
		return this.next( 1 ) ;
	}
}