CF1342E.Placing Rooks

Calculate the number of ways to place $n$ rooks on $n \times n$ chessboard so that both following conditions are met:

• each empty cell is under attack;
• exactly $k$ pairs of rooks attack each other.

An empty cell is under attack if there is at least one rook in the same row or at least one rook in the same column. Two rooks attack each other if they share the same row or column, and there are no other rooks between them. For example, there are only two pairs of rooks that attack each other in the following picture:

One of the ways to place the rooks for $n = 3$ and $k = 2$

Two ways to place the rooks are considered different if there exists at least one cell which is empty in one of the ways but contains a rook in another way.

The answer might be large, so print it modulo $998244353$.

计算在 $n \times n$ 棋盘上放置 $n$ 个车（rook）的方案数，使得同时满足以下两个条件：

• 每个空格均被攻击；
• 恰好有 $k$ 对车相互攻击。

一个空格被攻击，当且仅当其所在行或所在列中至少存在一个车。两个车相互攻击，当且仅当它们位于同一行或同一列，且二者之间（沿该行或该列方向）不存在其他车。例如，在下图中仅有两对车相互攻击：

当 $n = 3$、$k = 2$ 时的一种合法放法

若存在某个格子，在一种放法中为空、而在另一种放法中放置了车，则认为这两种放法不同。

答案可能很大，请对 $998244353$ 取模后输出。

The only line of the input contains two integers $n$ and $k$ ($1 \le n \le 200000$; $0 \le k \le \frac{n(n - 1)}{2}$).

输入仅包含一行，其中有两个整数 $n$ 和 $k$（$1 \le n \le 200000$；$0 \le k \le \frac{n(n - 1)}{2}$）。

Print one integer — the number of ways to place the rooks, taken modulo $998244353$.

输出一个整数——放置车的方法数，对 $998244353$ 取模。