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())
L = [X]
S = set([X])
idx = N
MOD = 10**9+7
for i in range(1,N):
  X = (X**2%M)
  if len(S) != len(L):
    idx = L.index(X)
    break
  L.append(X)
  S.add(X)

if idx == N:
  print(sum(L[:idx]))
else:
  k = (N-idx)%len(L[idx:])
  print(sum(L[:idx])+((N-idx)//len(L[idx:]))*sum(L[idx:])+sum(L[idx:idx+k]))