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]
A_dict = {X}
a = X
s = X
r = 0
r0 = 0
l = 0
amari = 0

for i in range(M+1):
  a = a ** 2 % M
  if a in A_dict:
    r0 = A.index(a)
    l = len(A[r0:])
    r = (N - i - 1) // l
    amari = (N - i - 1) % l
    s = s + sum(A[r0:])*r + sum(A[r0:r0+amari])
    break
  A.append(a)
  A_dict.add(a)
  s += A[-1]

print(s)