HDU-2604_Queuing

题目：Problem Description

Queues and Priority Queues are data structures which are known to most computer scientists. The Queue occurs often in our daily life. There are many people lined up at the lunch time. 

  Now we define that ‘f’ is short for female and ‘m’ is short for male. If the queue’s length is L, then there are 2^L numbers of queues. For example, if L = 2, then they are ff, mm, fm, mf . If there exists a subqueue as fmf or fff, we call it O-queue else it is a E-queue.
Your task is to calculate the number of E-queues mod M with length L by writing a program.

 

Input

Input a length L (0 <= L <= 10 ⁶) and M.

 

Output

Output K mod M(1 <= M <= 30) where K is the number of E-queues with length L.

 

Sample Input

3 8 4 7 4 8

 

Sample Output

6 2 1

 

Author

WhereIsHeroFrom

 

Source

HDU 1st “Vegetable-Birds Cup” Programming Open Contest

 

题目数据不强，正解应该是要矩阵快速幕，但是这不是我要说的重点

重点是推导过程：

如果F[N-1]：最后一项是M的话，就有ANS+=F[N-1];

如果是是L的话结果就是：ANS+=F[N-3]+MM,ANS+=F[N-3]+MF,其他的不符合，

但是F[N-3]+mf要考虑发 f[n-4]不能是F的情况，比较绕；结论是：

F[N-1]+M+F[N-3]+MMF+F[N-4]+FMMF+MMMF;