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 Python (3.8.2) (judge verdict: Runtime Error)

# import numpy as np
# import math
# import copy
# from collections import deque
import sys
input = sys.stdin.readline
# sys.setrecursionlimit(10000)


def main():
    N,X,M = map(int,input().split())

    A = [-1 for i in range(M)]
    A[0] = X

    for i in range(1,M):
        temp = A[i-1] ** 2
        temp %= M
        if temp in A:
            start = A.index(temp)
            end = i - 1
            break
        A[i] = temp

    # print(start,end)
    # print(A[start],temp)

    L = end - start + 1
    straight = [0 for i in range(start+1)]
    loop = [0 for i in range(L)]

    for i in range(start):
        straight[i] = straight[i-1] + A[i]

    for i in range(L):
        loop[i] = loop[i-1] + A[start+i]

    res = 0

    if start != 0:
        if N >= start:
            res += straight[-1]
            N -= start
        else:
            res += straight[N-1]
            N = 0

    res += (N // L) * loop[-1]

    if N % L != 0:
        res += loop[N % L - 1]

    print(res)



main()