Problem Statement

An integer sequence of length $N$ in which every element is an integer between $1$ and $M$, inclusive, is called a good integer sequence if it satisfies the following condition.

• Letting $A$ be the integer sequence, $\displaystyle \left | \left \lfloor \frac{M}{A_i} \right \rfloor - \left \lfloor \frac{M}{A_{i + 1}} \right \rfloor \right | \leq K$ holds for every integer $i$ satisfying $1 \leq i \leq N - 1$.

How many good integer sequences are there?

Since the answer can be very large, output it modulo $998244353$.

Constraints

• $1 \leq N \leq 10^{9}$
• $1 \leq M \leq 1000$
• $0 \leq K \leq M$
• All input values are integers.

Input

The input is given from standard input in the following format.

$N$ $M$ $K$ 

Output

Output the answer modulo $998244353$ on a single line.

Sample

2 3 1

5

100 100 38

412066770