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())
ans = 0
al = set([x])
for i in range(n):
  ans += x
  x = (x**2)%m
  if x==0:
    break
  if x in al:
    ind = list(al).index(x)
    loop = i-ind+1
    l = list(al)
    ans += sum(l[ind:i+1])*((n-i-1)//loop)
    for j in range((n-i-1)%loop):
      ans += l[ind+j]
    break
  al.add(x)
print(ans)