Kata

A numeral system is a way of writing numbers using a specific set of digits: for example, the decimal system (also called base-10), which is the most commonly used numeral system worldwide, uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to represent numbers. There is also the binary system (also called base-2), which uses the digits 0 and 1.

For digits that are bigger than 9, the English alphabet is used: 'A' is used for the number 10 in bases higher than 10. This goes all the way to 'Z' in base-36.

The largest digit allowed in a certain base is always 1 smaller than this base.

You need to write a function that checks whether all of the digits of a non-negative integer number are a part of the specified base: for example, the number 17253 is valid for base-8, because this base contains the digits 0, 1, 2, 3, 4, 5, 6, 7, but the number 19823 is not valid for this base, because it contains the digits 9 and 8 which are not a part of base-8.

Note: numbers will be checked against bases from 2 to 36. For digits > 9 (A, B, etc.) such digits will always be uppercase. The function should return a boolean: true for numbers that are valid for a specified numeral system and false otherwise.