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())
i = X % M
L = [i]
S = set([i])
i = i ** 2 % M
while not i in S:
    L.append(i)
    S.add(i)
    i = i ** 2 % M
index = L.index(i)
k = (N - index) // len(L[index:])
l = (N - index) % len(L[index:])

ans = sum(L[:index]) + (k * sum(L[index:]) + sum(L[index:index + l]))
print(ans)