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())

exist = [0 for _ in range(M)]


def f(a, m):
  return a % m

S = 0
A = X
ls = []
for n in range(1, N + 1):
  if exist[A] == 0:
    exist[A] = n
    ls.append(A)
  else:
    term = n - exist[A]
    loop = ls[-term:]
    res = N - n + 1
    S += (res // term) * sum(loop) + sum(loop[:res % term])
    break
  S += A
  A = f(A**2, M)

print(S)