Cherry isn't feeling well right now as she found a problem that she couldn't solve. So she started to listen to You and you, to make her happy, have to solve the problem for her.
You are given three integers $n, x$ and $m$.
Let $S = \sum\limits_{k \,=\, 0}^{n}{{{n}\choose{k}} \cdot x^{k \, \% \, m}}$. Here, $\%$ is the modulo operator.
You have to find the value of $S$ modulo $998,244,353$.
Input
The first and only line of the input contains three space-separated integers $n(1 \le n \le 10^{12})$, $x(1 \le x \lt 998,244,353)$ and $m(1 \le m \le 20,000)$.