hdu1757 A Simple Math Problem

Problem Description

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

If x < 10 f(x) = x.
If x >= 10 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 will give a0 ~ a9 and two 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 will be two lines.
In the first
line , there are two positive integers k and m. ( k<2*10^9 , m < 10^5
)
In the second line , there are ten integers represent a0 ~ a9.

 

Output

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

 

Sample Input

10 9999
1 1 1 1 1 1 1 1 1 1
20 500
1 0 1 0 1 0 1 0 1 0

 

Sample Output

45
104

/*
裸题
*/
#include<iostream>
#include<cstdio>
#include<string>
#include<cstring>
#include<algorithm>
#define ll long long
using namespace std;
const int maxn = ;
ll sz,mod,f[maxn],a[maxn],ans[maxn];
struct mtx{
    ll v[maxn][maxn];
    void clear(){
        memset(v,,sizeof(v));
    }
    mtx mul(mtx A,mtx B){
        mtx C;
        C.clear();
        for(int i = ;i <= sz;i++){
            for(int j = ;j <= sz;j++){
                for(int k = ;k <= sz;k++){
                    C.v[i][j] = (C.v[i][j] + A.v[i][k]*B.v[k][j]) % mod;
                }
            }
        }
        return C;
    }
    mtx pow(mtx A,int n){
        mtx R;
        R.clear();
        for(int i = ;i <= sz;i++) R.v[i][i] = ;
        while(n){
            if(n&) R = R.mul(R,A);
            n >>= ;
            A = A.mul(A,A);
        }
        return R;
    }
    void get_tr(mtx A){
        for(int i = ;i <= sz;i++){
            for(int j = ;j <= sz;j++){
                ans[j] = (ans[j] + f[i]*A.v[i][j]) % mod;
            }
        }
    }
};
int main(){
    ll d,n,m;
   while(scanf("%I64d%I64d",&n,&m) == ) {
       d = ;
       mtx A;
    for(int i = ; i <= d; i++) { cin >> a[i]; a[i] %= m; }
    for(int i = d; i >= ; i--) { f[i] = d-i; f[i] %= m; }
    if(n < ){
        cout<<n<<endl;
        continue;
    }
    n++;
    A.clear();
    memset(ans,,sizeof(ans));
    for(int i = ; i <= d; i++) A.v[i][] = a[i];
    for(int i = ; i <= d; i++) A.v[i-][i] = ;

    sz = d;
    mod = m;
    A = A.pow(A,n-d);
    A.get_tr(A);
    cout << ans[] << endl;
  }
    return ;
}