H. Make a wish!
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

If the person to your right and the person to your left have the same name, then you can make a wish. Your task is to arrange $$$n$$$ Andrews, $$$n$$$ Bens and $$$n$$$ Charlies in a row so that there are exactly $$$k$$$ people among them who can make a wish.

Input

The input contains two numbers $$$n$$$ and $$$k$$$, $$$(1 \leq n \leq 20000$$$, $$$0 \leq k \leq 3*n)$$$.

Output

If the necessary arrangement is impossible, print -1. Otherwise, output a string of $$$3*n$$$ characters. It must contain exactly $$$n$$$ characters $$$A$$$, $$$B$$$, $$$C$$$, each of which represents a person with the corresponding name. If there are more than one correct answers, print any of them.

Examples
Input
2 1
Output
CAABCB
Input
6 17
Output
-1