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(" "))
q = [-1] * (M + 1)
A = X
i = 0
su = []

while q[A] == -1:
    q[A] = i
    su.append(A)
    A = (A * A) % M
    i += 1

if N == len(su):
    print(sum(su))

else:
    r = q[A]
    r2 = (N - r) % (i - r)

    ans1 = sum(su[0:r])
    ans2 = sum(su[r:r + r2])
    ans3 = sum(su[r::])

    print(ans1 + ans2 + ans3 * (N // (i - r)))