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, tmp = X, X
s = set()
s.add(X)
for i in range(1, N):
  tmp = (tmp**2) % M
  if tmp == 0:
    break
  if tmp == 1:
    ans += N-i
    break
  if tmp not in s:
    s.add(tmp)
    ans += tmp
  else:
    s = list(s)
    idx = s.index(tmp)
    ans += sum(s[idx:]) * ((N-i)//(len(s)-idx))
    ans += sum(s[idx:idx+(N-i)%(len(s)-idx)])
    break
print(ans)