P17231 [Math×Girl²] Coloring⁴


You are given a $ka\times kb\times kc\times kd$ four-dimensional grid, where each cell can only be black or white. How many coloring schemes are there such that, in every $k\times k\times k\times k$ subgrid, there are **exactly** $1$ black cell? Since the answer may be very large, you only need to output the result modulo $998244353$.

The first line contains an integer $T$, the number of test cases. The next $T$ lines each contain five integers $k,a,b,c,d$, and it is guaranteed that $a\le b\le c\le d$.

Output $T$ lines, each containing one integer: the number of schemes modulo $998244353$.

### Sample Explanation See [Coloring³](https://www.luogu.com.cn/problem/P17230) for details. ### Constraints and Notes |Test Point|Score|$k$|$d$|Special Property| |:-:|:-:|:-:|:-:|:-:| |$1$| $1$|$k=1$| - | - | |$2$| $4$| - |$d=2$|$(a,b,c)=(2,2,2)$| |$3$| $5$| - |$d\le20$|^| |$4$| $5$|$k=2$| - |^| |$5$|$10$| - | - |^| |$6$| $5$|$k=2$| - |$(a,b,c)=(2,2,3)$| |$7$|$10$| - | - |^| |$8$| $5$|$k=2$| - |$(a,b,c)=(2,2,4)$| |$9$|$10$|$k=3$| - |^| |$10$|$10$|$k=2$| - |$(a,b,c)=(2,2,5)$| |$11$|$10$|$k=2$| - |$(a,b,c)=(2,2,6)$| |$12$|$5$|$k=2$| - |$(a,b,c)=(2,3,3)$| |$13$|$10$|$k=2$| - |$(a,b,c)=(2,3,4)$| |$14$|$10$|$k=2$| - |$(a,b,c)=(3,3,3)$| For $100\%$ of the testdata: $1\le T\le3$, $1\le k