Sum of Fibonacci Products

Given three integers l, r, and k, compute the following sum modulo 998244353:

\[ \sum_{i=l}^{r} \prod_{j=i}^{i+k-1} f_j \]

Here, the Fibonacci sequence \(\{f_n\}\) is defined as follows:

• \(f_0 = 0\)
• \(f_1 = 1\)
• \(f_n = f_{n-1} + f_{n-2}\) for \(n \ge 2\)

Your task is to output the sum modulo 998244353.

inputFormat

The input consists of a single line containing three space-separated integers l, r, and k.

outputFormat

Output a single integer — the value of the sum defined above modulo 998244353.

sample

0 5 1

12