F. AmShZ Farm
combinatorics; fft; math
To AmShZ, all arrays are equal, but some arrays are more-equal than others. Specifically, the arrays consisting of \(n\) elements from \(1\) to \(n\) that can be turned into permutations of numbers from \(1\) to \(n\) by adding a non-negative integer to each element.Mashtali who wants to appear in every problem statement thinks that an array \(b\) consisting of \(k\) elements is compatible with a more-equal array \(a\) consisting of \(n\) elements if for each \(1 \le i \le k\) we have \(1 \le b_i \le n\) and also \(a_{b_1} = a_{b_2} = \ldots = a_{b_k}\).Find the number of pairs of arrays \(a\) and \(b\) such that \(a\) is a more-equal array consisting of \(n\) elements and \(b\) is an array compatible with \(a\) consisting of \(k\) elements modulo \(998244353\).Note that the elements of \(b\) are not necessarily distinct, same holds for \(a\).
The first line of input contains two integers \(n\) and \(k\) \((1 \le n \le 10^9 , 1 \le k \le 10^5)\).
Print a single integer — the answer to the problem modulo \(998244353\).
There are eight possible pairs for the second example: \(a = \{1, 1\}, b = \{1, 1\}\) \(a = \{1, 1\}, b = \{1, 2\}\) \(a = \{1, 1\}, b = \{2, 1\}\) \(a = \{1, 1\}, b = \{2, 2\}\) \(a = \{1, 2\}, b = \{1, 1\}\) \(a = \{1, 2\}, b = \{2, 2\}\) \(a = \{2, 1\}, b = \{1, 1\}\) \(a = \{2, 1\}, b = \{2, 2\}\)