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())
D = {i:0 for i in range(M)}
L = [X]
c = X
D[X]=0
S = X
for i in range(1, N):
  c = (c**2)%M
  if D[c]==0:
    D[c] = i
    L.append(c)
    S += c
    continue
  else:
    p, q = D[c], i
    break
else:
  print(S)
  exit()  
cycle = L[p:q]
cycle_sum = sum(cycle)
cycle_num = (N-q)//(q-p)
rest = (N-q)%(q-p)
S += cycle_sum*cycle_num
S += sum(cycle[:rest])
print(S)