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}.

Examples

Input

6 2 1001


Output

1369


Input

1000 2 16


Output

6


Input

10000000000 10 99959


Output

492443256176507
import math
import sys
pin=sys.stdin.readline

def main():
  N,X,M=map(int,pin().split())
  A=X
  d=[X]
  su=X
  for i in range(N-1):
    A=(A**2)%M
    if A in d:
      t=d.index(A)
      T=N-i-1
      d=d[t:]
      l=len(d)
      su+=sum(d)*(T//l)
      T=T%(T//l)
      su+=sum(d[:T])
      print(su)
      return
    d.append(A)
    su+=A
  print(su)
  return
main()