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())
lst=[]
n,s=X,0
for i in range(N):
  if n in lst:break
  lst.append(n)
  n=(n*n)%M
if len(lst)<N:
  k=lst.index(n)
  s1=sum(lst[:k])
  s2=sum(lst[k:])*((N-k)//(len(lst)-k))
  s3=sum(lst[k:k+(N-k)%(len(lst)-k)])
  s=s1+s2+s3
else:s=sum(lst)
print(s)