Valid Integer Checker

This problem requires you to determine whether a given integer string x is valid under certain criteria.

An integer string x is valid if and only if:

1. Format Validity: The string must either be 0 or, if it is not 0, it must consist of an optional negative sign '-' followed by a digit between 1 and 9, and then followed by any number (possibly zero) of digits between 0 and 9. No extra leading zeros are allowed.
2. Range Constraint: The integer value represented by the string x must lie within the interval \([l, r]\), i.e., \(l \le x \le r\).

You will be given the bounds \(l\) and \(r\) and then several test cases. For each test case, check if the given string x is a valid integer under the above conditions.

inputFormat

The input begins with a line containing two integers \(l\) and \(r\). The second line contains an integer \(T\), representing the number of test cases. Each of the following \(T\) lines contains a string representing the integer x to be checked.

outputFormat

For each test case, output a single line. Print LEGAL if the string x is a well-formatted integer and its value is within the interval \([l, r]\); otherwise, print ILLEGAL.

sample

0 100
5
0
50
-1
001
100

LEGAL
LEGAL
ILLEGAL
ILLEGAL
LEGAL