1 /*UVA10870: 2 矩阵快速幂与递推公式的关系:关键就是这句话,以后做题能联想到即可 3 f(n)=a1f(n-1)+...adf(n-d) 4 */ 5 #include<iostream> 6 #include<stdio.h> 7 #include<string.h> 8 #include<algorithm> 9 #include<stdlib.h> 10 #include<math.h> 11 #include<queue> 12 #include<vector> 13 #include<map> 14 #define ULL unsigned long long 15 #define LL long long 16 #define Max_size 17 17 18 using namespace std; 19 20 int d,n,MOD;// 21 struct Mat 22 { 23 LL mat[Max_size][Max_size]; 24 25 }; 26 Mat operator*(Mat a,Mat b) 27 { 28 Mat c; 29 memset(c.mat,0,sizeof(c.mat)); 30 for (int i=0;i<d;i++) 31 for (int j=0;j<d;j++) 32 for (int k=0;k<d;k++) 33 if (a.mat[i][k] && b.mat[k][j]) 34 c.mat[i][j]=(c.mat[i][j]+a.mat[i][k]*b.mat[k][j])%MOD; 35 return c; 36 } 37 Mat operator+(Mat a,Mat b) 38 { 39 Mat c; 40 memset(c.mat,0,sizeof(c.mat)); 41 for (int i=0;i<d;i++) 42 for (int j=0;j<d;j++) 43 c.mat[i][j]=(a.mat[i][j]+b.mat[i][j])%MOD; 44 return c; 45 } 46 Mat E; 47 48 void builtE() 49 { 50 memset(E.mat,0,sizeof(E.mat)); 51 for (int i=0;i<Max_size;i++) 52 { 53 E.mat[i][i]=1; 54 } 55 } 56 Mat operator^(Mat A,int x) 57 { 58 Mat c; 59 builtE(); 60 c=E; 61 for ( ; x; x>>=1) 62 { 63 if ( x & 1) 64 c = c * A; 65 A = A * A; 66 } 67 return c; 68 } 69 Mat K,F; 70 int main() 71 { 72 while(cin>>d>>n>>MOD) 73 { 74 memset(K.mat,0,sizeof(K.mat)); 75 memset(F.mat,0,sizeof(F.mat)); 76 for(int i=d-1;i>=0;i--) cin>>K.mat[i][d-1]; 77 for(int i=0;i<d;i++) K.mat[i+1][i]=1; 78 K=K^(n-1); 79 for(int i=0;i<d;i++) cin>>F.mat[0][i]; 80 F=F*K; 81 cout<<F.mat[0][0]<<endl; 82 } 83 return 0; 84 }