Problem:
Score : 1100 points

Problem Statement

Let f(A, B), where A and B are positive integers, be the string satisfying the following conditions:

f(A, B) has length A + B;

f(A, B) contains exactly A letters A and exactly B letters B;

The length of the longest substring of f(A, B) consisting of equal letters (ex., AAAAA or BBBB) is as small as possible under the conditions above;

f(A, B) is the lexicographically smallest string satisfying the conditions above.

For example, f(2, 3) = BABAB, and f(6, 4) = AABAABAABB.

Answer Q queries: find the substring of f(A_i, B_i) from position C_i to position D_i (1-based).

Constraints

1 \leq Q \leq 10^3

1 \leq A_i, B_i \leq 5 \times 10^8

1 \leq C_i \leq D_i \leq A_i + B_i

D_i - C_i + 1 \leq 100

All input values are integers.

Partial Score

500 points will be awarded for passing the testset satisfying 1 \leq A_i, B_i \leq 10^3.

Input

Input is given from Standard Input in the following format:

Q
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
:
A_Q B_Q C_Q D_Q

Output

For each query i in order of input, print a line containing the substring of f(A_i, B_i) from position C_i to position D_i (1-based).

Sample Input 1

5
2 3 1 5
6 4 1 10
2 3 4 4
6 4 3 7
8 10 5 8

Sample Output 1

BABAB
AABAABAABB
A
BAABA
ABAB

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.File;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public char f(int a, int b, int pos, int mx) {
            Debug.print(a, b, pos, mx);
            if (a <= mx && b <= mx) {
                return pos < mx ? 'A' : 'B';
            }
            if (b > a) {
                return (char) (f(b, a, b + a - pos - 1, mx) ^ 'A' ^ 'B');
            }
            if (b == 0) return 'A';
            int lo = 0, hi = a / mx;
            while (lo < hi) {
                int mid = (lo + hi + 1) / 2;
                int useda = mid * mx;
                int usedb = mid;
                int lefta = a - useda;
                int leftb = b - usedb;

                if (lefta < 0 || leftb < 0) {
                    hi = mid - 1;
                    continue;
                }

                if (leftb > lefta * mx) {
                    hi = mid - 1;
                    continue;
                }

                lo = mid;
            }
            int useda = lo * mx;
            int usedb = lo;
            int lefta = a - useda;
            int leftb = b - usedb;

            if (pos < lo * (mx + 1)) {
                if (pos % (mx + 1) == mx) {
                    return 'B';
                } else {
                    return 'A';
                }
            }
            return f(lefta, leftb, pos - lo * (mx + 1), mx);
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int q = in.nextInt();
            while (q-- > 0) {
                int a = in.nextInt(), b = in.nextInt(), c = in.nextInt(), d = in.nextInt();
                for (int i = c; i <= d; i++) {
                    Debug.print(a, b, c, d, i);
                    out.print(f(a, b, i - 1, (a + b) / (Math.min(a, b) + 1)));
                }
                out.println();
            }
        }

    }

    static class Debug {
        public static boolean DEBUG;

        static {
            try {
                DEBUG = System.getProperty("user.dir").contains("Dropbox");
            } catch (Exception e) {
                DEBUG = false;
            }
        }

        private static ArrayList<String> getParams() {
            StackTraceElement[] t = new Exception().getStackTrace();
            StackTraceElement up = t[2];

            ArrayList<String> ret = new ArrayList<>();
            ret.add(up.getFileName() + "/" + up.getMethodName());
            try {
                BufferedReader br = new BufferedReader(new FileReader(
                        new File("src/" + up.getClassName().replaceAll("\\.", "/") + ".java")));
                int g = up.getLineNumber();
                while (--g > 0) br.readLine();
                String q = br.readLine();
                String[] ss = q.split("Debug\\.print\\(");
                String[] qq = ss[1].substring(0, ss[1].indexOf(")")).split(",");
                for (int i = 0; i < qq.length; i++) {
                    ret.add(qq[i].trim());
                }
            } catch (Exception e) {
            }
            for (int i = 0; i < 100; i++) ret.add("???");
            return ret;
        }

        private static String toString(Object o) {
            if (o instanceof Object[]) {
                return Arrays.toString((Object[]) o);
            } else if (o instanceof char[]) {
                return new String((char[]) o);
            } else if (o instanceof int[]) {
                return Arrays.toString((int[]) o);
            } else if (o instanceof long[]) {
                return Arrays.toString((long[]) o);
            } else if (o instanceof double[]) {
                return Arrays.toString((double[]) o);
            } else {
                return o.toString();
            }
        }

        public static void print(Object... x) {
            if (!DEBUG) return;
            ArrayList<String> s = getParams();
            System.out.print(s.get(0) + ": ");
            for (int i = 0; i < x.length; i++) {
                System.out.print(s.get(i + 1) + " = " + toString(x[i]));
                if (i != x.length - 1) System.out.print(", ");
            }
            System.out.println();
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void println() {
            writer.println();
        }

        public void print(char i) {
            writer.print(i);
        }

        public void close() {
            writer.close();
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (this.numChars == -1) {
                throw new InputMismatchException();
            } else {
                if (this.curChar >= this.numChars) {
                    this.curChar = 0;

                    try {
                        this.numChars = this.stream.read(this.buf);
                    } catch (IOException var2) {
                        throw new InputMismatchException();
                    }

                    if (this.numChars <= 0) {
                        return -1;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int c;
            for (c = this.read(); isSpaceChar(c); c = this.read()) {
                ;
            }

            byte sgn = 1;
            if (c == 45) {
                sgn = -1;
                c = this.read();
            }

            int res = 0;

            while (c >= 48 && c <= 57) {
                res *= 10;
                res += c - 48;
                c = this.read();
                if (isSpaceChar(c)) {
                    return res * sgn;
                }
            }

            throw new InputMismatchException();
        }

        public static boolean isSpaceChar(int c) {
            return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
        }

    }
}