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()
ct=x
ans=[x]
s.add(x)
f=0
for i in range(n-1):
  ct**=2
  ct%=m
  if ct not in s:
    s.add(ct)
    ans.append(ct)
  else:
    f=1
    break
if f==0:
  print(sum(ans))
  exit()
y=ans.index(ct)
z=sum(ans[y:len(ans)])
z2=0
for i in range(((n-y)%(len(ans)-y))):
  z2+=ans[y+i]
print(sum(ans[0:y])+z*((n-y)//(len(ans)-y))+z2)