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())

lim = 10**5+1

f = [0]*(lim)
a = [0]*(lim)

x = X
f[x] = 1
a[1] = x

ans = x

i = 1
l = N
while i < l:
    i += 1

    x **= 2
    x %= M
    if not x:
        break

    if f[x]:
        lp_len = (i-f[x])
        z = (l-i+1)//lp_len
        if z:
            ls = ans - a[f[x]-1]
            ans += ls * z
            i += z*lp_len

    if i < l:
        ans += x
    
    f[x] = i
    if i < lim:
        a[i] = ans

print(ans)