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
mod = [a]
loop = []
cnt = 0
while cnt < n:
    a = a**2 % m
    if a in mod:
        i = mod.index(a)
        before = mod[:i]
        loop = mod[i:]
        break
    mod.append(a)
    cnt += 1

length = len(loop)
if length == 0:
    print(sum(mod))
else:
    t = (n-i)//length
    amari = (n-i) % length
    ans = sum(before) + t * sum(loop) + sum(loop[:amari])
    print(ans)