Chilling capybaras celebrate Capybara Cozy Carnival. Chairman capybara cuts convex cake. Cake contains~$n$~colorful corners. Countless colors comprise $k$ choices. Creating $m$ continuous crossing-free corner-to-corner cuts, chairman cuts cake chunks, catering $m + 1$ comrades. Curiously, consecutive cake chunks corners contain contrasting colors. 

Calculate cake corners color combinations, considering cuts conditions.

In other words, you are given a cake in the shape of a regular $n$-sided polygon and $m$ non-intersecting diagonal cuts, which divide it into $m + 1$ slices.

Calculate the number of ways to color each corner of the original cake with one of the $k$ colors, such that no two neighboring corners of the resulting slices have the same color. Two corners are considered neighboring if they are either consecutive in the original cake, or they are the endpoints of the same cut. It~is not necessary to use all the colors. As the number of ways might be large, find it modulo $998\,244\,353$.