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())

am=[]

d={}

ch=0

for i in range(m):
  y=x%m
  
  if y==0:
    ch+=1
    break
  if y not in d:
    d[y]=0
    
    am.append(y)
    
    x=y*y
    
  else:
    stop=y
    break
    
if ch>0:
  st=0
  ans=0
  while st<=n-1 and st<=len(am)-1:
    ans+=am[st]
    st+=1
    
  print(ans)

else:
  for i in range(len(am)):
    if am[i]==y:
      now=i
      
  new_am=am[now:]
  s_new=sum(new_am)
  l=len(new_am)
  if n<i:
    print(sum(am[:n]))
    
  else:
    s=sum(am[:now])
    rest=n-now
    x=rest//l
    y=rest%l
    print(s+x*s_new+sum(new_am[:y]))