biinfinite

A bi-infinite sequence means a sequence that is infinite in both directions. In other words, it means a function whose domain is the set of all integers. The writer of this problem defined their bi-infinite sequence $(K\_n)\_{n\in\mathbb Z}$ and called it "KSA bi-infinite sequence" with a parameter $t$ where $t$ is a positive integer. It satisfies the following for all integers $n$.

• $K\_n=5701.5+0.5\cdot(-1)^n$ if $0\le n\<t$
• $K\_n=\sum\_{j=1}^t(t+1-j)K\_{n-j}$

Write a function biinfinite:

• input parameter: two int-type objects whose values are $t$ and $n$, respectively, where $1\le t\le 8$ and $|n|\le10^{12}$
• return value: the int-type object whose value is $\lfloor K\_n\rfloor-M\left\lfloor\frac{K\_n}M\right\rfloor$ where $M=202112210950$ and $K\_n$ is the $n$-th term of KSA bi-infinite sequence with a parameter $t$