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
from itertools import accumulate

N, X, M = map(int, input().split())
s = []
A = X
ind = {}
i = 0
while A not in ind:
    s.append(A)
    ind[A] = i
    A = A * A % M
    i += 1
L = i - ind[A]
s = [0] + list(accumulate(s))
ans = s[ind[A]] + (s[-1] - s[ind[A]]) * ((N - ind[A]) // L) + s[ind[A] + (N - ind[A]) % L] - s[ind[A]]
print(ans)