HDU 1757-a simple Math problem (Matrix fast power)

A Simple Math problemTime limit:MS Memory Limit:32768KB 64bit IO Format:%i64d &%i64u SubmitStatusPracticeHDU 1757Appoint Description:System Crawler (2015-03-04)

Description

Lele now was thinking about a simple function f (x).

If x < f (x) = x.
If x >= f (x) = a0 * F (X-1) + A1 * F (x-2) + A2 * F (x-3) + ... + A9 * F (x-10);
and AI (0<=i<=9) can only be 0 or 1.

Now, I'll give A0 ~ A9 and positive integers k and M, and could you help Lele to Caculate f (k)%m.

Input

The problem contains mutiple test cases. Please process to the end of file.
In each case, there'll be is the lines.
In the first line, there is, positive integers k and M. (K<2*10^9, M < 10^5)
In the second line, there is ten integers represent A0 ~ A9.

Output

For each case, output f (k)% m in one line.

Sample Input

Sample Output

Test instructions: It's two formulas.
If x < f (x) = x.
If x >= f (x) = a0 * F (X-1) + A1 * F (x-2) + A2 * F (x-3) + ... + A9 * F (x-10); evaluated.

Idea: This is a preliminary learning how to construct a matrix, in fact, there is nothing rare, mainly to think bad, alas, or too weak.

X<10 time to say, the following is the situation of n>=10. Such as

Matrix A matrix B


0 1 0 0 0 0 0 0 0 0 F0 F1


0 0 1 0 0 0 0 0 0 0 F1 f2


0 0 0 1 0 0 0 0 0 0 F2 f3


0 0 0 0 1 0 0 0 0 0 * F3----------> F4


0 0 0 0 0 1 0 0 0 0 f4 f5


0 0 0 0 0 0 1 0 0 0 f5 f6


0 0 0 0 0 0 0 1 0 0 f6 F7


0 0 0 0 0 0 0 0 1 0 F7 F8


0 0 0 0 0 0 0 0 0 1 F8 F9


A9 A8 A7 a6 A5 A4 A3 A2 A1 A0 F9 F10


We see the law, every time to the next a*b, and so on by a*a*a ... A*b;

#include <stdio.h> #include <math.h> #include <string.h> #include <stdlib.h> #include < iostream> #include <algorithm> #include <set> #include <map> #include <queue>using namespace std;const int Inf=0x3f3f3f3f;int mod;int a[20];struct node {int mp[20][20];} init,res;struct node Mult (struct node x,s    Truct node y) {struct node tmp;    int i,j,k;            For (i=0, i<10; i++) for (j=0; j<10; J + +) {tmp.mp[i][j]=0;            for (k=0; k<10; k++) {tmp.mp[i][j]= (tmp.mp[i][j]+x.mp[i][k]*y.mp[k][j])%mod; }} return tmp;};    struct Node Expo (struct node X,int k) {struct node tmp;    int i,j;            For (i=0, i<10; i++) for (j=0; j<10; J + +) {if (i==j) tmp.mp[i][j]=1;        else tmp.mp[i][j]=0;        } while (k) {if (k&1) Tmp=mult (tmp,x);        X=mult (X,X);    k>>=1; } return tmp;}; int main () {int k,x,i,j;    while (~SCANF ("%d%d", &k,&mod)) {if (k<10) {printf ("%d\n", k%mod);        Continue;        } for (i=9; i>=0; i--) a[i]=9-i;            for (i=0; i<10; i++) {scanf ("%d", &x);        Init.mp[0][i]=x%mod; } for (I=1, i<10; i++) {for (j=0; j<10; J + +) {if (i==j+1) init.mp I                [J]=1;            else init.mp[i][j]=0;        }} res=expo (init,k-9);        int ans=0;        for (j=0; j<10; J + +) {ans= (ans+res.mp[0][j]*a[j])%mod;    } printf ("%d\n", ans); } return 0;}

HDU 1757-a simple Math problem (Matrix fast power)