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=X
ls=[X]
point=N
for i in range(N):
  a=a*a%M
  if a in ls:
    point=ls.index(a)
    break
  else:
  	ls.append(a)
initial=len(ls[:point])
cycle_len=len(ls[point:])
cycle_sum=sum(ls[point:])
cycles=(N-initial)//cycle_len
cycles_rem=(N-initial)%cycle_len
print(sum(ls[:point])+cycles*cycle_sum+sum(ls[point:point+cycles_rem]))