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: Runtime Error)

n,x,m = map(int,input().split())
mod = m
ans = 0
bit = [-1 for i in range(m)]
cycle = False
for i in range(n):
    if i == 0 :
        a = x
        bit[a] = i
        ans += a
    else:
        a = (a**2)% mod
        if bit[a] != -1:
            cy_st = bit[a]
            cy_fi = i -1
            cycle = True
            break
        else:
            bit[a] = i
            ans += a

if cycle:
    ans2 = x
    a = x
    for j in range(1,cy_st):
        a = (a**2)% mod
        ans2 += a
    cy_num = ans - ans2
    cy_repe = (n-cy_st) // (cy_fi - cy_st + 1)
    ans3 = cy_num * cy_repe
    cy_amari = (n-cy_st) % (cy_fi - cy_st + 1)
    for i in range(cy_amari):
        a = (a**2)% mod
        ans3 += a

print(ans2+ans3)