P5853 [USACO19DEC] Tree Depth P

For the new year, Farmer John decided to give his cows a festive binary search tree (BST)! To generate the BST, FJ starts with a permutation $a=\{a_1,a_2,\ldots,a_N\}$ of the integers $1\ldots N$, where $N\le 300$. He then runs the following pseudocode with arguments $1$ and $N.$ ``` generate(l,r): if l > r, return empty subtree; x = argmin_{l

The only line of input consists of three space-separated integers $N,K$,and $M$, followed by a new line. $M$ will be a prime number in the range $[10^8,10^9+9]$.

Print $N$ space-separated integers denoting $\sum_a d_i(a) (\bmod M)$ for each $1\leq i\leq N$

### Sample Explanation For the first example,the only permutation is $a=\{1,2,3\}$. For the second example,the two permutations are $a=\{1,3,2\}$ and $a=\{2,1,3\}$. ### Data range Test cases $3-4$ satisfy $N\leq 8$. Test cases $5-7$ satisfy $N\leq 20$. Test cases $8-10$ satisfy $N\leq 50$.