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
import sys
input = sys.stdin.readline
N, X, M = map(int, input().split())
table = [0] * M
c = [0] * M
c[X] = 1
x = X
while table[x] <= 1:
  table[x] += 1
  if c[x ** 2 % M] == 0: c[x ** 2 % M] = c[x] + 1
  x = x ** 2 % M
loop = table.count(2)
#print(loop)
res = 0
for x in range(M):
  if c[x] in range(1, N + 1):
    res += x
    if c[x] + loop in range(1, N + 1) and (table[x] >= 2): res += x * ((N - c[x]) // loop)
print(res)