B (Region 2012)

#include <cstdio>
#include <iostream>
#include <string>

#define N 2005
#define INF int(1e6)

using namespace std;

int dp[N][N][2][2], m, n, add[2][2][2], res;
pair<int, int> from[N][N][2][2];
string s = "GB", answer;

void ans(int pos, int pos2, int ind1, int ind2) {
    if (pos > 1) {
        ans(pos - 1, from[pos][pos2][ind1][ind2].first, from[pos][pos2][ind1][ind2].second, ind1);
    }
    answer += s[ind1];
}

int main() {
    freopen("table.in", "r", stdin);
    freopen("table.out", "w", stdout);

    cin >> m >> n;

    add[0][1][0] = add[0][0][1] = add[1][0][0] = 1;

    for (int end1 = 0; end1 < 2; end1++)
        for (int end2 = 0; end2 < 2; end2++) {
            for (int i = 0; i < m + n; i++)
                for (int i2 = 0; i2 <= m; i2++) {
                    for (int k = 0; k < 2; k++)
                        for (int l = 0; l < 2; l++) {
                            dp[i][i2][k][l] = -INF;
                        }
                }

//          cout << "_______________\n";

            for (int j = 0; j < 2; j++)
                for (int k = 0; k < 2; k++) {
                    dp[1][j + k][j][k] = add[end1][end2][j] + add[end2][j][k];
//                  fprintf(stdout, "dp[1][%d][%d][%d] = %d\n", j + k, j, k, dp[1][j + k][j][k]);
            }

            for (int i = 2; i < m + n; i++)
                for (int i2 = 0; i2 <= m; i2++) {
                    for (int j = 0; j < 2; j++)
                        for (int k = 0; k < 2; k++)
                            for (int l = 0; l < 2; l++) {
                                int next = (l ? 1 : 0);
                                next += i2;

                                if (dp[i][next][k][l] < dp[i - 1][i2][j][k] + add[j][k][l]) {
                                    dp[i][next][k][l] = dp[i - 1][i2][j][k] + add[j][k][l];
//                                  fprintf(stdout, "dp[%d][%d][%d][%d] = %d\n", i, next, k, l, dp[i][next][k][l]);
                                    from[i][next][k][l] = make_pair(i2, j);
                                }
                            }
                }

                if (dp[n + m - 1][m][end1][end2] > res) {
                    res = dp[n + m - 1][m][end1][end2];
                    answer = "";
                    ans(n + m - 1, m, end1, end2);
                    answer += s[end2];
                }
        }
    cout << answer << endl;


    return 0;
}