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 PyPy3 (7.3.0) (judge verdict: Accepted)

import bisect
from collections import deque
import copy
import heapq
import sys
import itertools
import math
import queue
input = sys.stdin.readline
sys.setrecursionlimit(1000000)
# mod = 10 ** 9 + 7
mod = 998244353

def read_values(): return map(int, input().split())
def read_index(): return map(lambda x: int(x) - 1, input().split())
def read_list(): return list(read_values())
def read_lists(N): return [read_list() for n in range(N)]



def main():
    N, X, M = read_values()
    F = [-1] * (M + 1)

    A = X
    t = 0
    while F[A] < 0:
        F[A] = t
        A = pow(A, 2, M)
        t += 1
    
    if t == 1:
        print(X * N)
        return
    d = (N - F[A]) // (t - F[A])
    r = ((N - F[A]) % (t - F[A])) + F[A]

    K = 0
    for _ in range(F[A], t):
        K += A
        A = pow(A, 2, M)
    
    K *= d

    A = X
    for _ in range(r):
        K += A
        A = pow(A, 2, M)

    print(K)


if __name__ == "__main__":
    main()