Problem: There are n boys and m girls studying in the class. They should stand in a line so that boys and girls alternated there as much as possible. Let's assume that positions in the line are indexed from left to right by numbers from 1 to n + m. Then the number of integers i (1 ≤ i < n + m) such that positions with indexes i and i + 1 contain children of different genders (position i has a girl and position i + 1 has a boy or vice versa) must be as large as possible. 

Help the children and tell them how to form the line.

Input

The single line of the input contains two integers n and m (1 ≤ n, m ≤ 100), separated by a space.

Output

Print a line of n + m characters. Print on the i-th position of the line character "B", if the i-th position of your arrangement should have a boy and "G", if it should have a girl. 

Of course, the number of characters "B" should equal n and the number of characters "G" should equal m. If there are multiple optimal solutions, print any of them.

Examples

Input

3 3


Output

GBGBGB


Input

4 2


Output

BGBGBB

Note

In the first sample another possible answer is BGBGBG. 

In the second sample answer BBGBGB is also optimal.

Solution (in JAVA):

Solution:
import java.util.* ;
import java.io.* ;

public class Main {
	private int lim1 , lim2 , cn , ind , cc , n , a , b ; 
	private String[] brr ;
	private int arr[] ;
	private long crr[] ;
	private int memo[][] , done[][] ;
	
	public Main() {	
		this.ind = 1 ;		
		this.init() ;
	}
	
	private void init() {
		int i ;
		this.lim1 = 100100 ;
		this.lim2 = 110 ;
		this.cn = 0 ;
		this.cc = 1 ;
		this.arr = new int[ this.lim1 ] ;
		Arrays.fill( this.arr , 0 ) ;
		this.crr = new long[ this.lim1 ] ;
		Arrays.fill( this.crr , 0 ) ;
		this.memo = new int[ this.lim2 ][ this.lim2 ] ;		
		for( int zrr[] : this.memo ) {
			Arrays.fill( zrr , -1 ) ;
		}
		this.done = new int[ this.lim2 ][ this.lim2 ] ;
		for( int zrr[] : this.done ) {
			Arrays.fill( zrr , 1 ) ;
		}
		this.brr = new String[ this.lim1 ] ;
		for( i = 0 ; i < this.lim1 ; i++ ) {
			this.brr[ i ] = new String( "" ) ;
		}
	}
	
	public void clearPerCase() {	
		this.cc++ ;
		this.n = 0 ;
	}
	
	public void setCn( int c ) {
		this.cn = c ;  
	}
	
	public void incrementCn() {
		this.cn++ ;
	}
	
	public int getCn() {
		return this.cn ;
	}
	
	public boolean getInput( InputReader IH ) {
		int i ;
		try {
			this.a = IH.nextInt() ;
			this.b = IH.nextInt() ;
		}		
		catch( Exception ex ) {
			return false ;
		}
		return true ;
	}
	
	public String solveCase() {
		int i , j , tot ;
		String res ;
		boolean start ;
		res = new String( "" ) ;
		tot = this.a + this.b ;
		if( tot % 2 == 0 ) {
			if( this.a > this.b ) {
				start = false ;
			}
			else {
				start = true ;
			}
		}
		else {
			if( this.a > this.b ) {
				start = false ;
			}
			else {
				start = true ;
			}
		}
		for( i = 0 ; i < tot ; i++ ) {
			if( start == false ) {
				res += "B" ;
				this.a-- ;
			}
			else {
				res += "G" ;
				this.b-- ;
			}
			start = ! start ;
			if( start == false && this.a == 0 ) {
				start = true ;
			}
			else if( start == true && this.b == 0 ) {
				start = false ;
			} 
		}
		return res ;
	}
	
    public static void main( String[] args ) {
    	InputStream inputStream ;
    	OutputStream outputStream ;
    	inputStream = null ;
    	outputStream = null ;
        //inputStream = System.in ;
        //outputStream = System.out ;
    	try {
    		inputStream = new FileInputStream( "input.txt" ) ;
            outputStream = new FileOutputStream( "output.txt" ) ;    		
    	}
    	catch( Exception ex ) {
    	}
        InputReader IH = new InputReader( inputStream ) ;
        PrintWriter OH = new PrintWriter( outputStream ) ;        
        int n , a , b , i , T , ind ;
        String res ;
        Main MO ;
        try {
	        MO = new Main() ;
	        for( ind = 1 ;  ; ind++ ) {        	
	        	MO.clearPerCase() ;
	        	boolean end = MO.getInput( IH ) ;
	        	if( end == false ) {
	        		break ;
	        	}
	        	res = MO.solveCase() ;
	        	OH.println( res ) ;	        	
	        }        
        }
        catch( Exception ex ) {
        	ex.printStackTrace( OH ) ;
        	throw new RuntimeException( ex ) ;
        }
        finally {
        	OH.close() ;
        }
    }
}

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 ) ;
    }
}