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: Accepted)

N, X, M = map(int,input().split())
if N==1:
  print(X)
  exit()
a = [X]
sa = set([X])
for i in range(1,N):
  X = (X**2)%M
  if X in sa:
    break
  else:
    a.append(X)
    sa.add(X)

if i==N-1:
  print(sum(a))
  exit()
start = a.index(X)
ans = sum(a[:start])
base = sum(a[start:])
rep = i-start
sets = (N-start)//rep
more = (N-start)%rep
ans += base*sets + sum(a[start:start+more])
print(ans)