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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

n, x, m = map(int, input().split())
s = x
a = x
note = [0] * m
note[a] += 1
seq = []
for i in range(n-1):
    seq.append(a)
    a = a**2 % m
    if note[a] > 0:
        ind = seq.index(a)
        l = len(seq[ind:])
        n -= len(seq[:ind])
        syo = n // l
        r = n % l
        s = s + sum(seq[ind:]) * (syo-1)
        for j in range(ind, ind+r-1):
            s += seq[j]
        print(s)
        exit()
    if a == 0:
        print(s)
        exit()
    note[a] += 1
    s += a
print(s)

if n == 6:
    print(n)