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.StringTokenizer;

public class CodeForcesBase {
    static boolean local = false;

    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(new File("output.txt"));
        Scanner sc = local ? new Scanner(new FileReader("E:\\dev\\project\\JoshOJ\\src\\input")) : new Scanner(new FileInputStream(new File("input.txt")));

        while (sc.ready()) {
            handle(sc, out);
        }

        out.flush();
        out.close();
    }

    private static void handle(Scanner sc, PrintWriter out) throws IOException {
        int bn = sc.nextInt();
        int gn = sc.nextInt();
        if (bn > gn) {
            out.println(work(bn, gn, 'B', 'G'));
        } else {
            out.println(work(gn, bn, 'G', 'B'));
        }
    }

    private static String work(int n1, int n2, char c1, char c2) {
        StringBuilder sb = new StringBuilder();

        while (n2 > 0) {
            sb.append(c1);
            sb.append(c2);
            n1--;
            n2--;
        }
        while (n1 > 0) {
            sb.append(c1);
            n1--;
        }
        return sb.toString();
    }


    private static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }


    }
}