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())
sm=[-1 for i in range(m)]+[0]
w=[-1 for i in range(m)]
d=[m]
a=x
t=0
s=0
while True:
  s+=a
  if w[a]!=-1:
    inter=t-w[a]
    fv=w[a]
    ls=d[(n-fv)%inter+fv]
    lls=d[w[a]]
    print(sm[lls]+(n-fv)//inter*(s-sm[a])+(sm[ls]-sm[lls]))
    break
  w[a]=t
  d.append(a)
  sm[a]=s
  t+=1
  a=(a*a)%m