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. 

OutputFor each case, output f(k) % m in one line.Sample Input

10 99991 1 1 1 1 1 1 1 1 120 5001 0 1 0 1 0 1 0 1 0

Sample Output

45104 思路： 矩阵太大，用5*5的代为表达吧~

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