# A Simple Math Problem

Time Limit: 3000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 2791    Accepted Submission(s): 1659

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

代码：

``` 1 //#define LOCAL
2 #include<cstdio>
3 #include<cstring>
4 #define LL __int64
5 using namespace std;
6 const int maxn=10;
7 LL k,m;
8 int aa[maxn],mat[maxn][maxn];
9 int ans[maxn][maxn];
10
11 void init()
12 {
13     for(int i=0;i<10;i++)
14     {
15      for(int j=0;j<10;j++)
16      {
17        if(i==0)
18          mat[i][j]=aa[j];
19        else
20           if(i==j+1)mat[i][j]=1;
21        else mat[i][j]=0;
22        if(i==j)
23            ans[i][j]=1;
24        else ans[i][j]=0;
25      }
26     }
27 }
28
29 void Matrix(int a[][10],int b[][10])
30 {
31
32      int c[10][10];
33      for(int i=0;i<10;i++)
34      {
35          for(int j=0;j<10;j++)
36         {
37             c[i][j]=0;
38           for(int k=0;k<10;k++)
39            {
40             c[i][j]=(c[i][j]+a[i][k]*b[k][j])%m;
41           }
42         }
43      }
44     for(int i=0;i<10;i++)
45     {
46       for(int j=0;j<10;j++)
47       {
48         a[i][j]=c[i][j];
49       }
50     }
51 }
52
53 void pow(LL n)
54 {
55     while(n>0)
56     {
57         if(n&1) Matrix(ans,mat);
58         n>>=1L;
59         if(n==0)break;
60         Matrix(mat,mat);
61     }
62 }
63
64 int main()
65 {
66     #ifdef LOCAL
67      freopen("test.in","r",stdin);
68     #endif
69
70   while(scanf("%I64d%I64d",&k,&m)!=EOF)
71   {
72        for(int i=0;i<10;i++)
73        scanf("%d",aa+i);
74      if(k<10) printf("%I64d\n",k%m);
75      else
76      {
77        init();
78        pow(k-9);
79        int res=0;
80        for(int i=0;i<10;i++)
81         res=(res+(10-i-1)*ans[0][i])%m;
82        printf("%d\n",res);
83     }
84   }
85   return 0;
86 }```

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