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
import sys
n,x,m=map(int,input().split())
a=[0]*(m+2)
cnt=[0]*(m+2)
a[1],f=x,x
cnt[f]=1
if x==0:
  print(0)
  sys.exit()
for i in range(2,m+1):
  f=f*f%m
  a[i]=f
  if cnt[f]==0:
    cnt[f]=1
  else:
    break
ind=a[1:].index(f)+1
ans=sum(a[:ind])+sum(a[ind:i])*((n-ind+1)//(i-ind))
p=(n-ind+1)%(i-ind)
ans+=sum(a[ind:ind+p])
print(ans)