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())

R = [-1] * M
R[X % M] = 0
A = [0] + [X % M]
a = X
for i in range(1, N):
  a **= 2
  a %= M
  if R[a] == -1:
    R[a] = i
    A += [A[-1] + a]
  else:
    print(X - X % M + (A[-1] - A[R[a]]) * ((N - R[a]) // (i - R[a])) + A[R[a] + (N - R[a]) % (i - R[a])])
    exit()
print(A[-1] + X - X % M)