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: Wrong Answer)

import math

n, x, m = map(int, input().split())
ans = x % m
loop_lis = []
loop_num = 0
before_cnt = 1
while True:
    if before_cnt == n:
        print(ans)
        exit()
    tmp = pow(x, 2)
    if tmp >= m:
        loop_lis = [tmp % m]
        x = tmp
        break
    before_cnt += 1
    tmp %= m
    ans += tmp
    x = tmp
for i in range(1, m):
    if before_cnt + i == n:
        ans += loop_lis[-1]
        break
    tmp = pow(x, 2) % int(m)
    if loop_lis[0] == tmp:
        remain = (n - before_cnt) % len(loop_lis)
        loop_num = math.floor((n - before_cnt) / len(loop_lis))
        if remain == 0:
            ans += loop_num * loop_lis[-1]
        else:
            ans += loop_num * loop_lis[-1] + loop_lis[remain - 1]
        break
    loop_lis.append(tmp + loop_lis[-1])
    x = tmp
print(ans)