P5396 Stirling Numbers of the Second Kind · Sequence.

**Tester’s note: The program running time is greatly affected by judging load, and it may be slowed down during peak times.**

The Stirling number of the second kind $\begin{Bmatrix} n \\m \end{Bmatrix}$ denotes the number of ways to partition $n$ **distinct** elements into $m$ **identical** non-empty sets. Given $n, k$, for every integer $i \in [0, n]$, you need to compute $\begin{Bmatrix} i \\k \end{Bmatrix}$. Since the answer can be very large, you need to output it modulo $167772161$ ($2^{25}\times 5+1$, which is a prime).

One line with two positive integers $n, k$, as described above.

One line with $n+1$ non-negative integers. You need to output, in order, the values of $\begin{Bmatrix} 0 \\k \end{Bmatrix}, \begin{Bmatrix} 1 \\k \end{Bmatrix}, \begin{Bmatrix} 2 \\k \end{Bmatrix}, \dots, \begin{Bmatrix} n \\k \end{Bmatrix}$.

For $20\%$ of the testdata, $n \leqslant 1000$. For $100\%$ of the testdata, $1 \leqslant k, n < 131072$. Translated by ChatGPT 5