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
hist = [a]
indices = [-1]*M
indices[a] = 0
flag=0
for i in range(1,min(10**6,N)):
  a = a**2 % M
  if indices[a] != -1:
    idx = indices[a]
    flag=1
    break
  hist.append(a)
  indices[a] = i
  
if flag==0:
  print(sum(hist))
  exit()
  
cycle = hist[idx:]
margin = hist[:idx]
q,r = divmod((N-len(margin)),len(cycle))
print(sum(margin)+sum(cycle)*q+sum(cycle[:r]))