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]
x = (X**2)%M

while x not in A:
  A.append(x)
  x = (x**2)%M

if len(A) >= N:
  answer = sum(A[:N])
else:
  index = 0
  while A[index] != x:
    index += 1
  len_loop = len(A) - index
  num_loop = (N-index)//len_loop
  num_last = N - index - len_loop*num_loop
  answer = sum(A[:index]) + num_loop*sum(A[index:]) + sum(A[index:index+num_last])

print(answer)