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())
S = X
A = [X]
exists = [0]*M
exists[X] = 1

for i in range(2,N+1):
  A_i = (A[-1]*A[-1])%M
  A.append(A_i)
  S += A_i
  if exists[A_i] == 0:
    exists[A_i] = 1
  else:
    S -= A_i
    del A[-1]
    B = A[A.index(A_i):]
    S += ((N-len(A))//len(B))*sum(B) + sum(B[:((N-len(A))%len(B))])
    break

print(S)