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: 3.0 seconds
Memory limit: 512.0 MB

# Problem
We call an array $$$a$$$ of length $$$n$$$ fancy if for each $$$1 < i \le n$$$ it holds that $$$a_i = a_{i-1} + 1$$$.

Let's call $$$f(p)$$$ applied to a permutation$$$^\dagger$$$ of length $$$n$$$ as the minimum number of subarrays it can be partitioned such that each one of them is fancy. For example $$$f([1,2,3]) = 1$$$, while $$$f([3,1,2]) = 2$$$ and $$$f([3,2,1]) = 3$$$.

Given $$$n$$$ and a permutation $$$p$$$ of length $$$n$$$, we define a permutation $$$p'$$$ of length $$$n$$$ to be $$$k$$$-special if and only if:

- $$$p'$$$ is lexicographically smaller$$$^\ddagger$$$ than $$$p$$$, and
- $$$f(p') = k$$$.

Your task is to count for each $$$1 \le k \le n$$$ the number of $$$k$$$-special permutations modulo $$$m$$$.

$$$^\dagger$$$ A 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).

$$$^\ddagger$$$ A permutation $$$a$$$ of length $$$n$$$ is lexicographically smaller than a permutation $$$b$$$ of length $$$n$$$ if and only if the following holds: in the first position where $$$a$$$ and $$$b$$$ differ, the permutation $$$a$$$ has a smaller element than the corresponding element in $$$b$$$.

## Input Format
The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 2000$$$, $$$10 \le m \le 10^9$$$) — the length of the permutation and the required modulo.

The second line contains $$$n$$$ distinct integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \le p_i \le n$$$) — the permutation $$$p$$$.

## Output Format
Print $$$n$$$ integers, where the $$$k$$$-th integer is the number of $$$k$$$-special permutations modulo $$$m$$$.

## Examples
```input
4 666012
1 3 4 2
```
```output
1 0 1 1
```
-----
```input
3 10
3 2 1
```
```output
1 2 2
```
-----
```input
7 1000000000
7 2 1 3 5 4 6
```
```output
1 6 40 201 705 1635 1854
```
-----
```input
10 11
10 9 8 7 6 5 4 3 2 1
```
```output
1 9 9 0 1 5 5 0 1 0
```

## Note
In the first example, the permutations that are lexicographically smaller than $$$[1,3,4,2]$$$ are:

- $$$[1,2,3,4]$$$, $$$f([1,2,3,4])=1$$$;
- $$$[1,2,4,3]$$$, $$$f([1,2,4,3])=3$$$;
- $$$[1,3,2,4]$$$, $$$f([1,3,2,4])=4$$$.

Thus our answer is $$$[1,0,1,1]$$$.

In the second example, the permutations that are lexicographically smaller than $$$[3,2,1]$$$ are:

- $$$[1,2,3]$$$, $$$f([1,2,3])=1$$$;
- $$$[1,3,2]$$$, $$$f([1,3,2])=3$$$;
- $$$[2,1,3]$$$, $$$f([2,1,3])=3$$$;
- $$$[2,3,1]$$$, $$$f([2,3,1])=2$$$;
- $$$[3,1,2]$$$, $$$f([3,1,2])=2$$$.

Thus our answer is $$$[1,2,2]$$$.

Now solve the problem and return the code.