Problem: The employees of the R1 company often spend time together: they watch football, they go camping, they solve contests. So, it's no big deal that sometimes someone pays for someone else.

Today is the day of giving out money rewards. The R1 company CEO will invite employees into his office one by one, rewarding each one for the hard work this month. The CEO knows who owes money to whom. And he also understands that if he invites person x to his office for a reward, and then immediately invite person y, who has lent some money to person x, then they can meet. Of course, in such a situation, the joy of person x from his brand new money reward will be much less. Therefore, the R1 CEO decided to invite the staff in such an order that the described situation will not happen for any pair of employees invited one after another.

However, there are a lot of employees in the company, and the CEO doesn't have a lot of time. Therefore, the task has been assigned to you. Given the debt relationships between all the employees, determine in which order they should be invited to the office of the R1 company CEO, or determine that the described order does not exist.

Input

The first line contains space-separated integers n and m <image> — the number of employees in R1 and the number of debt relations. Each of the following m lines contains two space-separated integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi), these integers indicate that the person number ai owes money to a person a number bi. Assume that all the employees are numbered from 1 to n.

It is guaranteed that each pair of people p, q is mentioned in the input data at most once. In particular, the input data will not contain pairs p, q and q, p simultaneously.

Output

Print -1 if the described order does not exist. Otherwise, print the permutation of n distinct integers. The first number should denote the number of the person who goes to the CEO office first, the second number denote the person who goes second and so on.

If there are multiple correct orders, you are allowed to print any of them.

Examples

Input

2 1
1 2


Output

2 1 


Input

3 3
1 2
2 3
3 1


Output

2 1 3 

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 ;
	
	private void dfs( int u ) {
	    int i , v , sz ;
	    this.vis[ u ] = 1 ;
	    sz = this.adj_list[ u ].size() ;
	    for( i = 0 ; i < sz ; i++ ) {
	        v = this.adj_list[ u ].get( i ) ;
	        if( this.vis[ v ] == 0 ) {
	        	this.dfs( v ) ;
	        }
	    }
	    this.nrr[ this.cn ].setV( u ) ;
	    this.nrr[ this.cn ].setC( this.dist ) ;
	    this.dist++ ;
	    this.cn++ ;
	}
	
	private void dfs2( int u ) {
	    int i , v , sz ;
	    this.vis[ u ] = 1 ;
	    this.zrr[ this.cnt ] = u ;
	    this.cnt++ ;
	    sz = this.adj_list2[ u ].size() ;
	    for( i = 0 ; i < sz ; i++ ) {
	        v = this.adj_list2[ u ].get( i ) ;
	        if( this.vis[ v ] == 0 ) { 
	        	this.dfs2( v ) ;
	        }
	    }
	}
	
	public void solveCase( PrintWriter pwObj ) {
		int i , j , ma , u , v , a , x , sz ;
		int res ;
		res = 0 ;
		this.cn = 0 ;
		this.dist = 1 ;
		Arrays.fill( this.vis , 0 ) ;
		for( i = 1 ; i <= this.n ; i++ ) {
			if( this.vis[ i ] == 0 ) {
				this.dfs( i ) ;
			}
		}
		Arrays.sort( this.nrr , 0 , this.cn ) ;
		Arrays.fill( this.vis , 0 ) ;
		this.cnt = 0 ;
		for( i = 0 ; i < this.cn ; i++ ) {
			u = this.nrr[ i ].getV() ;
			if( this.vis[ u ] == 0 ) {
				this.dfs2( u ) ;
			}
		}
		for( i = 0 ; i < this.cnt ; i++ ) {
			if( i != 0 ) {
				pwObj.print( " " ) ;
			}
			pwObj.print( this.zrr[ i ] ) ;
		}
		pwObj.println( "" ) ;
	}
	
	private void init() {
		//default values
		this.lim1 = 50010 ;
		this.lim2 = 110 ;
		this.cc = 1 ;
		this.ind = 0 ;
		this.declareArrays() ;
		this.fillAllArrays() ;
	}
	
	public boolean getInput( InputReader irObj ) {
		int i , u , v ;
		try {
			this.n = irObj.nextInt() ;
		}
		catch( Exception ex ) {
			return false ;
		}
		this.m = irObj.nextInt() ;
		for( i = 0 ; i < this.m ; i++ ) {
			u = irObj.nextInt() ;
			v = irObj.nextInt() ;
			this.adj_list[ v ].add( u ) ;
			this.arr[ u ]++ ;
		}
		return true ;
	}
	
	private int lim1 , lim2 , cn , ind , cc , n , m , dist , cnt ; 
	private String[] srr ;
	private int[] arr , brr , zrr , vis ;
	private Node[] nrr ;
	private long[] lrr ;
	private int[][] memo , done ;
	private ArrayList< Integer >[] adj_list , adj_list2 ;
	
	public void clearPerCase() {
		int i ;
		this.incrementInd() ;
		this.incrementCc() ;
		this.n = 0 ;
		this.cn = 0 ;
		for( i = 0 ; i < this.lim1 ; i++ ) {
			this.adj_list[ i ] = new ArrayList< Integer >() ;
			this.adj_list2[ i ] = new ArrayList< Integer >() ;
		}
		Arrays.fill( this.arr , 0 ) ;
		Arrays.fill( this.brr , 0 ) ;
		Arrays.fill( this.vis , 0 ) ;
	}
	
	private void declareArrays() {
		//array declarations
		this.arr = new int[ this.lim1 ] ;
		this.brr = new int[ this.lim1 ] ;
		this.vis = new int[ this.lim1 ] ;
		this.zrr = 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 ] ;
		this.adj_list2 = new ArrayList[ this.lim1 ] ;
	}
	
	private void fillAllArrays() {
		int i ;
		//array initiations
		Arrays.fill( this.arr , 0 ) ;
		Arrays.fill( this.brr , 0 ) ;
		Arrays.fill( this.vis , 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 >() ;
			this.adj_list2[ 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 , c ;
	
	private Node() {
	}
	
	public Node( int vParam , int cParam ) {
		this.v = vParam ;
		this.c = cParam ;
	}
	
	public void setV( int vParam ) {
		this.v = vParam ;
	}
	
	public void setC( int cParam ) {
		this.c = cParam ;
	}
	
	public int getV() {
		return this.v ;
	}
	
	public int getC() {
		return this.c ;
	}
	
	public int compareTo( Node nParam ) {
		return - ( this.getC() - nParam.getC() ) ;
	}
}

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 ) ;
	}
}