13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6ab,

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

The only line of the in

Non-Intersecting Subpermutations

Examples