Problem Description

Compute the value of the following expression modulo $998244353$, where $x$ is a real number and all other variables involved are integers:

$$\sum_{n=1}^N \sum_{m=1}^M \sum_{k=0}^{m-1} \lfloor \dfrac{nk+x}{m}\rfloor$$

Input Format

Input one line containing two positive integers $N, M$ and one real number $x$.

Output Format

Output one line containing one integer, representing the answer modulo $998244353$.

2 3 1 

7

Hint

Constraints: $1\leq N, M\leq 500000$, $0<x\leq 100000$. The value of $x$ is given accurate to $8$ digits after the decimal point.

Translated by ChatGPT 5