CF1861E.Non-Intersecting Subpermutations
普及/提高-
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题目描述
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 .
输入格式
The only line of the input contains two integers n and k ( 2≤k≤n≤4000 ).
输出格式
Print one integer — the sum of costs of all arrays of length n consisting of integers from 1 to k taken modulo 998244353 .
输入输出样例
输入#1
10 3
输出#1
71712
输入#2
2 2
输出#2
2
输入#3
1337 42
输出#3
524933698