Description

The clever rabbit defines three functions:

• $g(x)$ denotes the number formed by arranging the digits of the decimal representation of $x$ in descending order.
• $l(x)$ denotes the number formed by arranging the digits of the decimal representation of $x$ in ascending order.
• $f(x)=g(x)-l(x)$.

If a number $x$ equals $f(x)$, the rabbits call it a lucky number. Now the rabbits want to compute the sum of squares of all lucky numbers among all $n$-digit numbers. Output the result modulo $p$. Note that numbers may contain leading $0$s.

Input Format

One line with two integers $n,p$.

Output Format

One line with one integer, the required result.

4 10000

8276

Hint

Constraints

• For $20\%$ of the testdata, it is guaranteed that $1 \leq n \leq 10$.
• For $100\%$ of the testdata, it is guaranteed that $1 \leq n \leq 30$, $1 \leq p \leq 2 \times 10^9$.

Translated by ChatGPT 5