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
p=0
l=[x]
if x%m==0:
  print(x)
else:
  for i in range(1,n):
    s=(l[i-1]**2)%m
    if s==0:
      p=1
      break
    if s in l:
      p=2
      break
    else:
      l.append(s)
  if p==2:
    t=sum(l[1:])
    k=(n-1)//(len(l)-1) #ループ何回回るか
    j=(n-1)%(len(l)-1)
    ans=x+t*k+sum(l[1:j+1])
    print(ans)
  elif p==1:
    print(sum(l))
  else:
    print(sum(l))