_{This problem is a programming version of Problem 162 from projecteuler.net}

In the hexadecimal number system numbers are represented using different digits:

The hexadecimal number AF when written in the decimal number system equals .

In the hexadecimal numbers and the digits and are all present.

Like numbers written in base ten we write hexadecimal numbers without leading zeroes.

How many hexadecimal numbers containing at most hexadecimal digits exist with all of the digits and present at least once?

Give your answer modulo .