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 = list(map(int, input().split()))

A = X
sum_A = A
A_list = [X]
for i in range(1, N):
    A = A ** 2 % M

    if (A in A_list):
        start = A_list.index(A)
        loop = A_list[start:]
        sum_A += sum(loop)*((N-i)//len(loop)) + sum(loop[:(N-i) % len(loop)])
        break
    else:
        A_list.append(A)
    sum_A += A

    if (A == 0):
        break

print(sum_A)
