HDU4565/2013年长沙赛区So easy

Description

A sequence S_n is defined as:

Where a,b,n,m are positiveintegers.┌x┐is the ceil ofx. For example, ┌3.14┐=4. You are tocalculateS_n.

You, a top coder, say: So easy!

 

Input

There are several test cases, each testcase 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 integerS_n.

 

Sample Input
2 3 1 2013
2 3 2 2013
2 2 1 2013

 

Sample Output
4
14
4

 

#include <stdio.h>
void mmul(int a[2][2],int b[2][2],int c[2][2],int m){
int d[2][2],i,j,k;
for(i=0;i<2;++i)for(j=0;j<2;++j)for(k=d[i][j]=0;k<2;++k)d[i][j]=(d[i][j]+((a[i][k]*b[k][j])%m))%m;
for(i=0;i<2;++i)for(j=0;j<2;++j)c[i][j]=d[i][j];}
void mpow(int a[2][2],int b,int c[2][2],int m){
int t[2][2],d[2][2],i,j;
for(i=0;i<2;++i)for(j=0;j<2;++j){d[i][j]=a[i][j]%m;t[i][j]=i==j?1:0;}
while(b){
if(b&1)mmul(t,d,t,m);
mmul(d,d,d,m);
b>>=1;}
for(i=0;i<2;++i)for(j=0;j<2;++j)c[i][j]=t[i][j];}

int main(){
freopen("easy.in", "r", stdin);
freopen("testeasy.out", "w", stdout);
int a,b,m,n,c[2][2],r,i,j;
while(scanf("%d%d%d%d",&a,&b,&n,&m)!=EOF){
c[1][0]=1;c[1][1]=0;c[0][0]=(a<<1)%m;c[0][1]=(b-((a*a)%m))%m;
mpow(c,n-1,c,m);
r=(((((((c[0][0]*2)%m)*a)%m)+(c[0][1]*2)%m)%m)+m)%m;
printf("%d\n",r);}
return 0;}