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=set()
p=[]
while x not in s:
  s.add(x)
  p+=[x]
  x=(x*x)%m
  if len(p)>=n:print(sum(p));quit()
r=b=t=v=0
a=[0]
for i in p:
  if i==x:b=1
  r+=1-b
  t+=b*i
  v+=i
  a+=[a[-1]+i]*b
l=len(p)
print(v+t*((n-l)//(l-r))+a[(n-l)%(l-r)])