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())

a = []
check = [-1] * m
i = 0
while check[x] == -1:
  a.append(x)
  check[x] = i
  x = x * x % m
  i += 1
if n <= i:
  print(sum(a[:n]))
else:
  print(
    sum(a[:check[x]])
    + (n - check[x]) // (i - check[x]) * sum(a[check[x]:])
    + sum(a[check[x] : check[x] + (n - check[x]) % (i - check[x])]))