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: Time Limit Exceeded)

using System;
using static System.Console;
using System.Linq;
using System.Collections.Generic;

namespace AC
{
    class shiokara
    {
        static void Main(string[] args)
        {
            var tmp = ReadLine().Split(' ').Select(long.Parse).ToArray();
            long N = tmp[0], X = tmp[1], M = tmp[2];
            long ans = X;
            for(long i = 2; i <= N; i++){
                X = f(X, M);
                ans += X;
            }
            WriteLine(ans);
        }

        static long f(long An, long M)
        {
            return An * An % M;
        }
    }
}