You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 1024.0 MB

# Problem
Recall that the permutation 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).

A sequence $$$a$$$ is a subsegment of a sequence $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. We will denote the subsegments as $$$[l, r]$$$, where $$$l, r$$$ are two integers with $$$1 \le l \le r \le n$$$. This indicates the subsegment where $$$l-1$$$ elements from the beginning and $$$n-r$$$ elements from the end are deleted from the sequence.

For a permutation $$$p_1, p_2, \ldots, p_n$$$, we define a framed segment as a subsegment $$$[l,r]$$$ where $$$\max\{p_l, p_{l+1}, \dots, p_r\} - \min\{p_l, p_{l+1}, \dots, p_r\} = r - l$$$. For example, for the permutation $$$(6, 7, 1, 8, 5, 3, 2, 4)$$$ some of its framed segments are: $$$[1, 2], [5, 8], [6, 7], [3, 3], [8, 8]$$$. In particular, a subsegment $$$[i,i]$$$ is always a framed segments for any $$$i$$$ between $$$1$$$ and $$$n$$$, inclusive.

We define the happiness of a permutation $$$p$$$ as the number of pairs $$$(l, r)$$$ such that $$$1 \le l \le r \le n$$$, and $$$[l, r]$$$ is a framed segment. For example, the permutation $$$[3, 1, 2]$$$ has happiness $$$5$$$: all segments except $$$[1, 2]$$$ are framed segments.

Given integers $$$n$$$ and $$$m$$$, Jongwon wants to compute the sum of happiness for all permutations of length $$$n$$$, modulo the prime number $$$m$$$. Note that there exist $$$n!$$$ (factorial of $$$n$$$) different permutations of length $$$n$$$.

## Input Format
The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 250\,000$$$, $$$10^8 \le m \le 10^9$$$, $$$m$$$ is prime).

## Output Format
Print $$$r$$$ ($$$0 \le r < m$$$), the sum of happiness for all permutations of length $$$n$$$, modulo a prime number $$$m$$$.

## Examples
```input
1 993244853
```
```output
1
```
-----
```input
2 993244853
```
```output
6
```
-----
```input
3 993244853
```
```output
32
```
-----
```input
2019 993244853
```
```output
923958830
```
-----
```input
2020 437122297
```
```output
265955509
```

## Note
For sample input $$$n=3$$$, let's consider all permutations of length $$$3$$$:

- $$$[1, 2, 3]$$$, all subsegments are framed segment. Happiness is $$$6$$$.
- $$$[1, 3, 2]$$$, all subsegments except $$$[1, 2]$$$ are framed segment. Happiness is $$$5$$$.
- $$$[2, 1, 3]$$$, all subsegments except $$$[2, 3]$$$ are framed segment. Happiness is $$$5$$$.
- $$$[2, 3, 1]$$$, all subsegments except $$$[2, 3]$$$ are framed segment. Happiness is $$$5$$$.
- $$$[3, 1, 2]$$$, all subsegments except $$$[1, 2]$$$ are framed segment. Happiness is $$$5$$$.
- $$$[3, 2, 1]$$$, all subsegments are framed segment. Happiness is $$$6$$$.

Thus, the sum of happiness is $$$6+5+5+5+5+6 = 32$$$.

Now solve the problem and return the code.