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]
su=x
s={x}
for i in range(n-1):
  x=(x**2)%m
  if x in s:
    n-=i+1
    a=a[a.index(x):]
    l=len(a)
    su+=sum(a)*(n//l)
    n-=(n//l)*l
    su+=sum(a[:n])
    print(su)
    exit()
  a.append(x)
  su+=x
  s.add(x)
print(su)