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())
ary=[x]
ans=x
d={x:0}
i=1
while x and i<n and (x**2)%m not in d:
  x=(x**2)%m
  ans+=x
  d[x]=i
  ary.append(x)
  i+=1
if x==0 or i==n:
  print(ans)
  exit()
s=d[(x**2)%m]
l=i-s
suml=sum(ary[s:])
tmp=n-i
ans+=suml*(tmp//l)
ans+=sum(ary[s:s+tmp%l])
print(ans)