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())
ans = 0
a = x
arr = []
for i in range(n):
  if a in arr:
    break
  else:
    arr.append(a)
  a = a ** 2 % m
f = sum(arr[:arr.index(a)])
r = sum(arr[arr.index(a):])
k = (n - arr.index(a)) // (len(arr) - arr.index(a))
b = sum(arr[arr.index(a): arr.index(a) + (n - (arr.index(a) + (len(arr) - arr.index(a)) * k))])
ans = f + r * k + b
print(ans)