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())
Q=0
for i in range(min(100,N)):
  Q+=X
  X=X*X%M
N-=min(N,100)
S=set([X])
P=X
A=X
R=0
for i in range(M):
  A=A*A%M
  if A in S:
    R=i+1
    break
  S.add(A)
  P+=A
P*=(N//R)
N%=R
for i in range(N):
  P+=X
  X=X*X%M
print(P+Q)
