Problem:
Score : 500 points

Problem Statement

Let us denote by f(x, m) the remainder of the Euclidean division of x by m.

Let A be the sequence that is defined by the initial value A_1=X and the recurrence relation A_{n+1} = f(A_n^2, M).
Find \displaystyle{\sum_{i=1}^N A_i}.

Constraints

1 \leq N \leq 10^{10}

0 \leq X < M \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N X M

Output

Print \displaystyle{\sum_{i=1}^N A_i}.

Sample Input 1

6 2 1001

Sample Output 1

1369

The sequence A begins 2,4,16,256,471,620,\ldots Therefore, the answer is 2+4+16+256+471+620=1369.

Sample Input 2

1000 2 16

Sample Output 2

6

The sequence A begins 2,4,0,0,\ldots Therefore, the answer is 6.

Sample Input 3

10000000000 10 99959

Sample Output 3

492443256176507

Solution in C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
class Program
{
    static void Main(string[] args)
    {
        string a = Console.ReadLine(); //標準入力
        string[] aa = a.Split(' ');


        int N = int.Parse(aa[0]);
        decimal X = decimal.Parse(aa[1]);
        decimal M = decimal.Parse(aa[2]);
        decimal[] A = new decimal[N];
        A[0] = X;
        decimal count = X;
        for(int i = 0; i < N-1; i++)
        {
            A[i + 1] = amari(A[i], M);
            count += A[i + 1];
        }

        Console.WriteLine("{0}", count);
    }

    static decimal amari(decimal A ,decimal M)
    {
        return (A*A) % M;
    }
}