Description

We call a sequence of length $2n$ interesting if and only if it satisfies the following three conditions:

1. It is a permutation $\{a_i\}$ of the $2n$ integers from $1$ to $2n$;
2. All odd-indexed terms satisfy $a_1\lt a_3\lt \cdots \lt a_{2n-1}$, and all even-indexed terms satisfy $a_2\lt a_4\lt \cdots \lt a_{2n}$;
3. Any two adjacent terms $a_{2i-1}$ and $a_{2i}(1\le i\le n)$ satisfy that the odd-indexed term is less than the even-indexed term, i.e., $a_{2i-1}\lt a_{2i}$.

The task is: For a given $n$, determine how many different interesting sequences of length $2n$ exist. Since the final answer may be very large, only output the answer modulo $P$.

Input Format

The input contains only two integers $n$ and $P$ separated by a space.

Output Format

Output a single integer, representing the number of different interesting sequences of length $2n$ modulo $P$.

Sample 1

The corresponding $5$ interesting sequences are $\{1,2,3,4,5,6\},\{1,2,3,5,4,6\},\{1,3,2,4,5,6\},\{1,3,2,5,4,6\},\{1,4,2,5,3,6\}$.

3 10

5

Data Range and Hints

For $50\%$ of the data, $n\le 1000,P\le 10^6$;
For all data, $1\le n\le 10^6,2\le P\le 10^9$.