| [NightHawk22 - Isolation](https://soundcloud.com/vepium/nighthawk22-isolation- official-limbo-remix) | |
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| This is the medium version of the problem. In the three versions, the constraints on $n$ and the time limit are different. You can make hacks only if all the versions of the problem are solved. | |
| This is the statement of Problem D1B: | |
| * There are $n$ cities in a row, numbered $1, 2, \ldots, n$ left to right. * At time $1$, you conquer exactly one city, called the starting city. * At time $2, 3, \ldots, n$, you can choose a city adjacent to the ones conquered so far and conquer it. | |
| You win if, for each $i$, you conquer city $i$ at a time no later than $a_i$. A winning strategy may or may not exist, also depending on the starting city. How many starting cities allow you to win? | |
| For each $0 \leq k \leq n$, count the number of arrays of positive integers $a_1, a_2, \ldots, a_n$ such that | |
| * $1 \leq a_i \leq n$ for each $1 \leq i \leq n$; * the answer to Problem D1B is $k$. | |
| The answer can be very large, so you have to calculate it modulo a given prime $p$. | |
| Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 500$). The description of the test cases follows. | |
| The only line of each test case contains two integers $n$, $p$ ($1 \le n \le 500$, $10^8 \leq p \leq 10^9$, $p$ is prime) — the number of cities and the modulo. | |
| It is guaranteed that the sum of $n$ over all test cases does not exceed $500$. | |
| For each test case, output $n+1$ integers: the $i$-th integer should be the number of arrays that satisfy the conditions for $k = i-1$. | |
| In the first test case, | |
| * arrays with $1$ good starting city: $[1]$. | |
| In the second test case, | |
| * arrays with $0$ good starting cities: $[1, 1]$; * arrays with $1$ good starting city: $[1, 2]$, $[2, 1]$; * arrays with $2$ good starting cities: $[2, 2]$. | |
| In the third test case, | |
| * arrays with $0$ good starting cities: $[1, 1, 1]$, $[1, 1, 2]$, $[1, 1, 3]$, $[1, 2, 1]$, $[1, 2, 2]$, $[1, 3, 1]$, $ |