Description: Consider a permutation$$$^\dagger$$$ $$$p$$$ of length $$$3n$$$. Each time you can do one of the following operations: - Sort the first $$$2n$$$ elements in increasing order. - Sort the last $$$2n$$$ elements in increasing order. We can show that every permutation can be made sorted in increasing order using only these operations. Let's call $$$f(p)$$$ the minimum number of these operations needed to make the permutation $$$p$$$ sorted in increasing order. Given $$$n$$$, find the sum of $$$f(p)$$$ over all $$$(3n)!$$$ permutations $$$p$$$ of size $$$3n$$$. Since the answer could be very large, output it modulo a prime $$$M$$$. $$$^\dagger$$$ A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array). Input Format: The only line of input contains two numbers $$$n$$$ and $$$M$$$ ($$$1 \leq n \leq 10^6$$$, $$$10^8 \leq M \leq 10^9$$$). It is guaranteed that $$$M$$$ is a prime number. Output Format: Output the answer modulo $$$M$$$. Note: In the first test case, all the permutations are: - $$$[1, 2, 3]$$$, which requires $$$0$$$ operations; - $$$[1, 3, 2]$$$, which requires $$$1$$$ operation; - $$$[2, 1, 3]$$$, which requires $$$1$$$ operation; - $$$[2, 3, 1]$$$, which requires $$$2$$$ operations; - $$$[3, 1, 2]$$$, which requires $$$2$$$ operations; - $$$[3, 2, 1]$$$, which requires $$$3$$$ operations. Therefore, the answer is $$$0+1+1+2+2+3=9$$$.