Full analysis on paper, too lazy to write on the blog
I am a konjac, only the source code
#include<iostream> #include<stdio.h> #include<string.h> using namespace std; typedef long long LL; const int maxn=107; LL mod; struct mat{ LL m[maxn][maxn]; int X, y; /// X is the row number and y is the number of columns } Unit; void init_unit () { memset(unit.m,0,sizeof(unit.m)); for(int i=0;i<maxn;i++) unit.m[i][i]=1; } void show(mat a){ for(int i=1;i<=a.x;i++){ for(int j=1;j<=a.y;j++) printf("%d ",a.m[i][j]); printf("\n"); } } food mat_mul (food A, food b) { mat c; c.x=a.x,c.y=b.y; memset(c.m,0,sizeof(c.m)); for(int i=1;i<=c.x;i++) for(int j=1;j<=c.y;j++){ for(int k=1;k<=a.y;k++){ c.m[i][j]+=(a.m[i][k]*b.m[k][j])%(mod-1); c.m[i][j]%=mod-1; } } return c; } mat mat_QuickPow(mat a,LL b){ matt years = unites; ans.x=a.x,ans.y=a.y; while(b){ if(b&1) years = mat_mul (years,); a = mat_mul (a, a); b>>=1; } return years; } LL QuickPow(LL a,LL b){ LL ans=1; while(b){ if(b&1)ans=(ans*a)%mod; a=(a*a)%mod; b>>=1; } return years; } int t; LL n,x,y,z; int main () { scanf("%d",&t); init_unit(); while(t--){ scanf("%I64d%I64d%I64d%I64d%I64d",&n,&x,&y,&z,&mod); mat a; x = y = 3 ; a.m[1][1]=1,a.m[1][2]=y,a.m[1][3]=0; a.m[2][1]=0,a.m[2][2]=z,a.m[2][3]=1; a.m[3][1]=0,a.m[3][2]=1,a.m[3][3]=0; if(n==1){ printf("1\n"); continue; } if(n==2){ printf("%I64d\n",QuickPow(x,y)); continue; } a=mat_QuickPow(a,n-2); LL t=(a.m[1][2]+a.m[2][2]*y); printf("%I64d\n",QuickPow(x,t)); } return 0; }