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())
A = [X]
ret = X
k = X
for i in range(N):
  k = (k * k) % M
  ret += k
  
  if k in A:
    A.append(k)
    break
  A.append(k)
if len(A) == N:
  print(ret)
else:
  i = A.index(A[-1])
  s_rep = sum(A[i:-1])
  a_rep = A[i:-1]
  s_init = sum(A[:i])
  k = len(a_rep)
  l_ = N - i
  ret = s_init + s_rep * (l_ // k) +sum( a_rep[:(l_ % k)])
  print(ret)