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 OCaml (4.02.3) (judge verdict: Wrong Answer)

let () =
  let q = Scanf.scanf "%d\n" (fun q -> q) in
  let abcds = Array.init q (fun _ -> Scanf.scanf "%d %d %d %d\n" (fun a b c d -> a, b, c, d)) in
  Array.iter (fun (a, b, c, d) ->
    begin match compare a b with
    | -1 ->
        for i = c to d do
          (a + b - i) mod ((b + a) / (a + 1) + 1) < (a + b) / (a + 1)
          |> (function true -> 'B' | false -> 'A')
          |> print_char
        done
    | 0 ->
        for i = c to d do
          i mod 2 = 1
          |> (function true -> 'A' | false -> 'B')
          |> print_char
        done
    | 1 ->
        for i = c to d do
          (i - 1) mod ((a + b) / (b + 1) + 1) < (a + b) / (b + 1)
          |> (function true -> 'A' | false -> 'B')
          |> print_char
        done
    end;
    print_newline ()) abcds