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())

ans = 0
A = []
T = [-1]*M
i = 0
f = False
while i<N:
  if T[X]!=-1 and not f:
    f = True
    ans += sum(A[T[X]:])*((N-i)//(i-T[X]))
    i += (N-i)//(i-T[X])*(i-T[X])
    continue
  A += [X]
  T[X] = i
  ans += X
  X = X*X%M
  i += 1
print(ans)
