hdu So Easy!

So Easy!

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2026    Accepted Submission(s): 624

Problem Description

　　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 2013

2 3 2 2013

2 2 1 2013

 

Sample Output

4

14

4

 

Source

2013 ACM-ICPC长沙赛区全国邀请赛——题目重现

 #include<iostream>
 #include<stdio.h>
 #include<cstring>
 #include<cstdlib>
 using namespace std;
 typedef __int64 LL;

 LL  p ;
 struct Matrix
 {
     LL mat[][];
     void init()
     {
         mat[][]=;mat[][]=;
         mat[][]=;mat[][]=;
     }
     void mem(LL a,LL b)
     {
         mat[][]=(*a)%p; mat[][]=(b-a*a)%p;
         mat[][]=;     mat[][]=;
     }
 };
 Matrix multiply(Matrix cur,Matrix ans)
 {
     Matrix now;
     memset(now.mat,,sizeof(now.mat));
     int i,j,k;
     for(i=;i<=;i++)
     {
         for(k=;k<=;k++)
         {
             for(j=;j<=;j++)
             {
                 now.mat[i][j]+=cur.mat[i][k]*ans.mat[k][j];
                 now.mat[i][j]%=p;
                 while(now.mat[i][j]<) now.mat[i][j]+=p;
             }
         }
     }
     return now;
 }
 void pow_mod(Matrix cur,LL n,LL a,LL b)
 {
     Matrix ans;
     ans.init();
     while(n)
     {
         if(n&) ans=multiply(ans,cur);
         n=n>>;
         cur=multiply(cur,cur);
     }
     LL sum=(ans.mat[][]**a+ans.mat[][]*)%p;
     printf("%I64d\n",sum);
 }
 int main()
 {
     LL a,b,n;
     while(scanf("%I64d%I64d%I64d%I64d",&a,&b,&n,&p)>)
     {
         Matrix hxl;
         hxl.mem(a,b);
         if(n>)
         pow_mod(hxl,n-,a,b);
         else printf("%I64d\n",(*a)%p);
     }
     return ;
 }