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.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException{
        Scanner s = new Scanner(new File("input.txt"));
        int n = s.nextInt();
        int m = s.nextInt();
        StringBuilder ans = new StringBuilder();

        for (int i = 0; i < Math.max(m, n); i++) {
            if (n > m){
                ans.append("B");
                if (i < m) ans.append("G");
            }
            else {
                ans.append("G");
                if (i < n) ans.append("B");
            }
        }
        PrintWriter pw = new PrintWriter("output.txt");
        pw.println(ans.toString());
        pw.close();
    }

}

///**
// * Reader class based on the article at "https://www.cpe.ku.ac.th/~jim/java-io.html"
// * */
//class Reader{
//    private static BufferedReader reader;
//    private static StringTokenizer tokenizer;
//    static void init(InputStream inputStream){
//        reader = new BufferedReader(new InputStreamReader(inputStream));
//        tokenizer = new StringTokenizer("");
//    }
//    static String next() throws IOException {
//        String read;
//        while (!tokenizer.hasMoreTokens()){
//            read = reader.readLine();
//            if (read == null || read.equals(""))
//                return "-1";
//            tokenizer = new StringTokenizer(read);
//        }
//
//        return tokenizer.nextToken();
//    }
//    static int nextInt() throws IOException{
//        return Integer.parseInt(next());
//    }
//
//    static long nextLong() throws IOException{
//        return Long.parseLong(next());
//    }
//
//    //Get a whole line.
////    static String line() throws IOException{
////        return reader.readLine();
////    }
////
////    static double nextDouble() throws IOException{return Double.parseDouble(next());}
//}