Description: You are given two integers $$$n$$$ and $$$k$$$. For an array of length $$$n$$$, let's define its cost as the maximum number of contiguous subarrays of this array that can be chosen so that: - each element belongs to at most one subarray; - the length of each subarray is exactly $$$k$$$; - each subarray contains each integer from $$$1$$$ to $$$k$$$ exactly once. For example, if $$$n = 10$$$, $$$k = 3$$$ and the array is $$$[1, 2, 1, 3, 2, 3, 2, 3, 1, 3]$$$, its cost is $$$2$$$ because, for example, we can choose the subarrays from the $$$2$$$-nd element to the $$$4$$$-th element and from the $$$7$$$-th element to the $$$9$$$-th element, and we can show that it's impossible to choose more than $$$2$$$ subarrays. Calculate the sum of costs over all arrays of length $$$n$$$ consisting of integers from $$$1$$$ to $$$k$$$, and print it modulo $$$998244353$$$. Input Format: The only line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le k \le n \le 4000$$$). Output Format: Print one integer — the sum of costs of all arrays of length $$$n$$$ consisting of integers from $$$1$$$ to $$$k$$$ taken modulo $$$998244353$$$. Note: None