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
from collections import deque

N, X, M = map(int, input().split())

D = deque([X], M)
R = {X: 0}

x = X
for _ in range(min(N-1, M+1)):
  x = (x ** 2) % M
  if x in R:
    l = R[x]
    m = len(D) - l
    q, r = divmod(N - l, m)
    print(sum(D[i] for i in range(l)) + (q+1) * sum(D[i] for i in range(l, l+r)) + q * sum(D[i] for i in range(l+r, l+m)))
    break
  else:
    R[x] = len(D)
    D.append(x)
else:
  print(sum(D))
