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 f(x, m):
    return (x**2) % m

N, X, M = map(int, input().split())
A = [X]
S = {X}
while True:
    X = f(X, M)
    if X in S:
        break
    else:
        A.append(X)
        S.add(X)


start = A.index(X)
l = len(A) - start
ans = sum(A[:start])
N -= start

ans += sum(A[start:]) * (N//l)
N %= l

ans += sum(A[start:start+N])
print(ans)