Alternating Fruit Pattern Grid

You are given two integers \(r\) and \(c\) representing the number of rows and columns respectively. Your task is to generate a grid where each cell is filled with either the letter A (representing an apple) or B (representing a banana) in an alternating pattern.

The rule to determine the character at position \((i, j)\) (0-indexed) is:

[ \text{char}_{ij} = \begin{cases} A & \text{if } (i+j) \mod 2 = 0, \ B & \text{if } (i+j) \mod 2 = 1. \end{cases} ]

Print the generated grid with each row on a new line.

inputFormat

The input is read from standard input (stdin) and consists of one line containing two integers:

• r (1 ≤ r ≤ 1000): The number of rows.
• c (1 ≤ c ≤ 1000): The number of columns.

The two numbers are separated by spaces.

outputFormat

Output to standard output (stdout) the generated grid consisting of r lines. Each line is a string of length c where the character is either A or B following the alternating pattern as described.

## sample

3 4

ABAB
BABA
ABAB

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