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())
checklist = [True] * 100000
ind = 0
l = [X]
while True:
  t = l[-1] ** 2 % M
  if checklist[t]:
    l.append(t)
    checklist[t] = False
  else:
    ind = l.index(t)
    break
S = sum(l[ind:])
L = len(l)
ans = 0
if N <= L:
  ans = sum(l[:N])
else:
  ans = sum(l)
  N -= L
  ans += S * (N // (L - ind))
  ans += sum(l[ind:ind+(N % (L - ind))])
print(ans)