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.*;
import java.util.*;

public class Main {
	static final StdIn in = new StdIn();
	static final PrintWriter out = new PrintWriter(System.out);
	
	public static void main(String[] args) {
		int q=in.nextInt();
		while(q-->0) {
			int a=in.nextInt(), b=in.nextInt(), c=in.nextInt()-1, d=in.nextInt()-1, e=1;
			while(a>=b?(a-1)/e>b:(b-1)/e>a) 
				++e;
			char[] s = new char[a+b];
			for(int i=0, lastSame=0; i<s.length; ++i) {
				if(lastSame>=e) {
					if(s[i-1]=='A') {
						s[i]='B';
						--b;
					} else {
						s[i]='A';
						--a;
					}
					lastSame=1;
				} else {
					if(a-1>=b?(a-2)/e<=b:(b-1)/e<=a-1) {
						s[i]='A';
						if(i>0&&s[i-1]=='A')
							++lastSame;
						else
							lastSame=1;
						--a;
					} else {
						s[i]='B';
						if(i>0&&s[i-1]=='B')
							++lastSame;
						else
							lastSame=1;
						--b;
					}
				}
			}
			out.println(new String(s).substring(c, d+1));
		}
		out.close();
	}
	
	interface Input {
		public String next();
		public String nextLine();
		public int nextInt();
		public long nextLong();
		public double nextDouble();
	}
	static class StdIn implements Input {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;
		public StdIn() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
		public StdIn(InputStream in) {
			try{
				din = new DataInputStream(in);
			} catch(Exception e) {
				throw new RuntimeException();
			}
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
		public String next() {
			int c;
			while((c=read())!=-1&&(c==' '||c=='\n'||c=='\r'));
			StringBuilder s = new StringBuilder();
			while (c != -1)
			{
				if (c == ' ' || c == '\n'||c=='\r')
					break;
				s.append((char)c);
				c=read();
			}
			return s.toString();
		}
		public String nextLine() {
			int c;
			while((c=read())!=-1&&(c==' '||c=='\n'||c=='\r'));
			StringBuilder s = new StringBuilder();
			while (c != -1)
			{
				if (c == '\n'||c=='\r')
					break;
				s.append((char)c);
				c = read();
			}
			return s.toString();
		}
		public int nextInt() {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
				ret = ret * 10 + c - '0';
			while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}
		public int[] readIntArray(int n) {
			int[] ar = new int[n];
			for(int i=0; i<n; ++i)
				ar[i]=nextInt();
			return ar;
		}
		public long nextLong() {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
				ret = ret * 10 + c - '0';
			while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
		public long[] readLongArray(int n) {
			long[] ar = new long[n];
			for(int i=0; i<n; ++i)
				ar[i]=nextLong();
			return ar;
		}
		public double nextDouble() {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
				ret = ret * 10 + c - '0';
			while ((c = read()) >= '0' && c <= '9');
			if (c == '.')
				while ((c = read()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);
			if (neg)
				return -ret;
			return ret;
		}
		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}
		private byte read() {
			try{
				if (bufferPointer == bytesRead)
					fillBuffer();
				return buffer[bufferPointer++];
			} catch(IOException e) {
				throw new RuntimeException();
			}
		}
		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}
}