hdoj 1757 A Simple Math Problem

A Simple Math Problem

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

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

 思路：裸的矩阵快速幂，首先要构造矩阵

[fn]         [XXX]        [fn-1]

[fn-1]   = [XXX]  *    [fn-2]

[fn-2]      [XXX]        [fn-3]

……            ……            ……    

思考一下就可以得到

[fn]         [a0 a1 a2]        [fn-1]

[fn-1]   = [1  0   0]  *    [fn-2]

[fn-2]      [ 0  1  0 ]        [fn-3]

……            ……            ……