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())
amr = []
for i in range(n):
    if i == 0:
        x %= m
        amr.append(x)
        continue
    x = pow(x, 2, m)

    if x in amr:
        print('----', i)
        break
    if x == 0:
        break
    amr.append(x)

if x == 0:
    print(sum(amr[:n]))
else:
    idx = amr.index(x)

    loop = sum(amr[idx:])
    l = len(amr[idx:])

    if n >= idx:
        cnt = (n-idx)//l
        print(cnt*loop + sum(amr[:idx]) + sum(amr[idx:idx+n-idx-cnt*l:]))
    else:
        print(sum(amr[:n]))