i have a question why can t we go directly down from the start to the end i think it s one possible way to get there but they didn t take that under consideration

That was quite interesting. First I misread the condititions and thaugt m is limited by 6. So I hardcoded some data to solve the problem. When I saw my mistake I replaced the hardoded data by an algorithm which finds these data. But for 7 and 8 I timed out (in a large scale). Then I discovered that I do sparse matrix multiplications, so I optimized my code for it and managed to solve everything for m=7 and some of m=8. The worst case for m=8 needed nearly 20s. Finally I found a further optimization to solve everything n time.

any other output accept 6? which is accepted in submition?

how output should be printed..in power form?

Is there any way for the first tile hit on the bottom row to not be the bottom right?