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())
tmp = X
seq = []
ans = 0
for i in range(N):
  if X in seq:
    break
  seq.append(X)
  X = (X ** 2) % M

ans = sum(seq[:min(N, len(seq))])
N -= len(seq)
if N < 1:
    print(ans)
    exit()
i = seq.index(X)
l = len(seq) - i
ans += sum(seq[i:]) * (N//l)
N %= l
ans += sum(seq[i:i+N])
print(ans)
