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())
a = [X]

start_loop = 0
end_loop = 0

for n in range(N - 1):
        tmp = a[n]*a[n]%M
        if(tmp in a):
                start_loop = a.index(tmp)
                end_loop = n
                break
        a.append(tmp)

if start_loop:
        loop_num = end_loop - start_loop + 1

        sum_before_loop = sum(a[:start_loop])
        sum_loop = sum(a[start_loop: end_loop + 1])*int((N - start_loop)/ loop_num)
        sum_after_loop = sum(a[start_loop: start_loop+ (N - start_loop) % loop_num])
        print(int(sum_before_loop + sum_after_loop + sum_loop))
else:
        sum_before_loop = sum(a)
        print(sum_before_loop)