A Simple Math Problem

Time Limit: 3000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 1697    Accepted Submission(s): 959

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

 

 

Author

linle

 

 

Source

 

 

Recommend

lcy

 

 

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);

|f(10) |       |a0 a1 a2 ...a8 a9|    |f(9)|

| f(9)  |       | 1   0   0 ... 0    0 |    |f(8)|

| .....  |   =  | ..    ...    ...   ...    |    | .. |

| f(2) |        | 0   0   0 ... 0    0|     |f(1)|

| f(1) |　　 | 0   0   0 ... 1    0|     |f(0)|

另A举证为10*10的举证，如上图。

可以推出：

(f(n),f(n-1),...,f(n-9))^(-1) = A^(n-9)*(f(9),f(8),...,f(0))^(-1)

 

#include
     
      #include
      
       #include
       
        using namespace std;long long k,mod;struct Matrix{    int m[15][15];};Matrix unit,init;void Init(){    memset(init.m,0,sizeof(init.m));    for(int i=1;i<10;i++)        init.m[i][i-1]=1;    memset(unit.m,0,sizeof(unit.m));    for(int i=0;i<10;i++)        unit.m[i][i]=1;}Matrix Mul(Matrix a,Matrix b){    Matrix c;    for(int i=0;i<10;i++)        for(int j=0;j<10;j++){            c.m[i][j]=0;            for(int k=0;k<10;k++)                c.m[i][j]+=(a.m[i][k]*b.m[k][j])%mod;            c.m[i][j]%=mod;        }    return c;}Matrix Pow(Matrix a,Matrix b,int x){    while(x){        if(x&1){            b=Mul(a,b);        }        a=Mul(a,a);        x>>=1;    }    return b;}int main(){    //freopen("input.txt","r",stdin);    while(cin>>k>>mod){        Init();        for(int i=0;i<10;i++)            scanf("%d",&init.m[0][i]);        if(k<10){            cout<
        
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