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())

visited = [-1] * (M + 1)
x = X
i = 0
while visited[x] == -1 :
  visited[x] = i
  x = x * x % M
  i += 1

loop_l = i - visited[x]
loop_s = x

ret = 0
x = X
while x != loop_s :
  ret += x
  x = x * x % M
  N -= 1
  if N == 0 : break
    
if N > 0 :
  i = 0
  while i != loop_l :
    ret += x * ((N - i + loop_l - 1) // loop_l)
    x = x * x % M
    i += 1
  
print(ret)