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)

n, x, m = map(int, input().split())
ans = 0
prev_set = set()
prev_list = list()
ans_hist = list()
r = x

for i in range(n):
    if i == 0:
        pass
    else:
        r = (r * r) % m
    
    if r == 0:
        break
    
    if r in prev_set:
        index = prev_list.index(r)
        period = i - index
        count = (n - index) // period
        rest = (n - index) % period

        # ans = sum(prev_list[:index])
        # ans += sum(prev_list[index:i]) * count
        if index == 0:
            ans *= (count - 1)
        else:
            ans += (ans - ans_hist[index - 1]) * (count - 1)

        ans += sum(prev_list[index:index+rest])
        # ans += (ans_hist[index + rest - 1] - ans_hist[index - 1])
        break
    else:
        ans += r
        prev_set.add(r)
        prev_list.append(r)
        ans_hist.append(ans)
print(ans)