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
n,x,m=map(int,input().split())
A=[[0]*2 for i in range(m)]
A[x]=[1,x]
a=x
f=-1
for i in range(10**5+100):
  if i==n-1:
    f=0
    break
  x=x**2%m
  a=a+x
  if A[x][0]!=0:
    f=1
    break
  A[x]=[i+2,a]
if f==0:
  print(a)
elif f==1:
  ans=A[x][1]+(a-A[x][1])*((n-A[x][0])//(i+2-A[x][0]))
  for i in range((n-A[x][0])%(i+2-A[x][0])):
    x=x**2%m
    ans=ans+x
  print(ans)