Odd-Even Sorted Sequence

Given two integers \(n\) and \(m\), select \(m\) numbers from the set \(\{1,2,\ldots,n\}\) and sort them in increasing order to form a sequence \(p\). The sequence \(p\) is considered valid if every element at an odd index (1-indexed) is an odd number and every element at an even index is an even number.

Formally, let \(p = [p_1, p_2, \ldots, p_m]\). Then for all \(i\):

\[ \begin{aligned} p_i \;\text{is odd, if } i \;\text{is odd},\\ p_i \;\text{is even, if } i \;\text{is even}. \end{aligned} \]

Output the number of valid sequences modulo \(998\,244\,353\).

inputFormat

The first and only line of input contains two space-separated integers \(n\) and \(m\).

outputFormat

Output a single integer, the number of valid sequences modulo \(998\,244\,353\).

sample

5 3

6