no name

Subject:
https://ac.nowcoder.com/acm/problem/14532

Each population has $N$ different individuals form a circle and grow every other unit time.
In a unit time, each individual will radiate energy to both sides, the radiation range and intensity are both$K$ , the radiation intensity will decrease as the distance increases, and the distance increases by$1$ Radiation intensity decreased$1.$ The energy received through radiation in this unit time will be retained, and the initial energy will be consumed. For two individuals$a$，$b$ , where$a$ tobbThe radiation of$b$ will make$b$ increase [radiation intensity$\times a$ the initial energy value]. The overall change can be expressed as
$$a_i^{{}^{\prime }}=\sum _{j=1}^n[K-dis(i,j)>0][i\ne j](K-dis(i,j))a[j]$$

Idea: It
can be found that this is a linear transformation, and the coefficients are all determined.
$\mathbf{A}\left[\begin{array}{c}{a}_1\\ a_2\\ .\\ .\\ a_n\end{array}\right]=\left[\begin{array}{c}{a}_1^{{}^{\prime }}\\ a_2^{{}^{\prime }}\\ .\\ .\\ a_n^{{}^{\prime }}\end{array}\right]$
$A$ is a$n\ast$The matrix of$n$ is determined by the question formula. But this matrix multiplication is$O\left(n^4\right)$, you will find that each row of this matrix is ​​cyclic, and the multiplication of two circulant matrices is still a circulant matrix, so you only need to calculate the first row for each calculation, and the next few rows are obtained through the cycle.