Problem Statement

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 $\displaystyle{\sum_{i=1}^N A_i}$.