Problem Link: https://www.luogu.com.cn/problem/P10254
1. Problem Statement:
Given a permutation $$$p$$$ of length $$$n$$$, define $$$Inv(p)$$$ to be the inversion number of $$$p$$$ and $$$W(p) := \sum\limits_{i=1}^n ip_i$$$. For example, if $$$p = [1, 2, 3]$$$, the $$$W(p) = 1 \times 1 + 2 \times 2 + 3 \times 3 = 14$$$. Given integers $$$n$$$ and $$$k$$$, compute
$$$\sum\limits_{p \in S_n, Inv(p) = k} W(p)$$$