Solve the programming task below in a Python markdown code block.
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.

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).

Example

Input

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


Output

BABAB
AABAABAABB
A
BAABA
ABAB