2013 ACM-ICPC长沙赛区全国邀请赛So Easy! && 2015 ACM/ICPC Asia Regional Shenyang Online-Best Solver

<span style="background-color: transparent; color: rgb(124, 169, 237); font-family: Arial; font-size: 18px;">So Easy!</span>

　　A sequence S_n is defined as:

Where a, b, n, m are positive integers.┌x┐is the ceil of x. For example, ┌3.14┐=4. You are to calculate S_n.
　　You, a top coder, say: So easy! 

 

Input

　　There are several test cases, each test case in one line contains four positive integers: a, b, n, m. Where 0< a, m < 2¹⁵, (a-1)²< b < a², 0 < b, n < 2³¹.The input will finish with the end of file.

 

Output

　　For each the case, output an integer S_n.

 

Sample Input

2 3 1 20132 3 2 20132 2 1 2013

 

Sample Output

4144

 

4

那么用矩阵快速幂就可以了，代码如下：

Best Solver

Problem Description

The so-called best problem solver can easily solve this problem, with his/her childhood sweetheart.

It is known that y=(5+26√)1+2x.
For a given integer x (0≤x<232) and a given prime number M (M≤46337), print [y]%M. ([y] means the integer part of y)

 

Input

An integer T (1<T≤1000), indicating there are T test cases.
Following are T lines, each containing two integers x and M, as introduced above.

 

Output

The output contains exactly T lines.
Each line contains an integer representing [y]%M.

 

Sample Input

70 463371 463373 463371 4633721 46337321 463374321 46337

 

Sample Output

Case #1: 97Case #2: 969Case #3: 16537Case #4: 969Case #5: 40453Case #6: 10211Case #7: 17947

 

此题的a、b完全满足上题的要求，可用与上题完全相同的思路求解，唯一的不同点即为时向下取整而非向上取整，那么，在上题的答案基础上，减一，就是此题的答案。

　　还有就是指数太大，要找到循环节，其实由于mod小，循环节并没有太大，是可以搞的。

代码如下：