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=set()
b=[x]
for i in range(m):
  x=pow(x,2,m)
  if x in a:break
  a.add(x)
  b+=[x]
j=b.index(x)
n-=j
c=b[j:]
ans=sum(b[:j])+sum(c)*(n//len(c))+sum(c[:n%len(c)])
print(ans)