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

def main():
    N, X, M = map(int, input().split())
    Set = {X}
    A = [X]
    for i in range(1,M+1):
        nextA = A[i-1]**2 % M
        if nextA in Set:
            loop = A[A.index(nextA):]
            break
        else:
            Set.add(nextA)
            A.append(nextA)

    lenloop = len(loop)
    x, y = divmod(N-len(A), lenloop)
    ans = sum(A) + x*sum(loop) + sum(loop[0:y])
    print(ans)

main()
