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
from sys import stdin
import copy

def main():
    input = stdin.readline
    n, x, m = map(int, input().split())
    a = np.array([x], dtype=np.int64)
    h = {}
    h[x] = 0
    t = 0
    for i in range(n - 1):
        t = a[i] * a[i] % m
        if t in h:
            break
        h[t] = 0
        a = np.append(a, t)
    b = copy.deepcopy(a)
    a = a[:np.where(a == t)[0][0]]
    b = np.setdiff1d(b, a)
    ans = sum(a)
    if len(b) > 0:
        ans += sum(b) * ((n - len(a)) // len(b))
        ans += sum(b[0: (n - len(a)) % len(b)])
    print(int(ans))
main()