最大值 - 問題

#10933. 最大值

統計

この問題は以下のコンテストで使用されています：

Elegia's Forgotten Hill

This problem is prepared by Elegia .

Nasshitaka4692 现在有 $n$ 个变量 $a_1,\dots,a_n$ 初始为 $0$，接下来他会做 $k$ 轮操作。每次他会等概率随机选择一个变量并将其 $+1$。他想知道 $\max \{a_1,\dots,a_n\}$ 的期望。你只需要帮他求出这个期望值乘以 $n^k$ 的结果，同余 $998244353$。

输入格式

输入两个正整数 $n,k$。

输出格式

输出一个数，表示答案。

样例数据

样例 1 输入

2 5

样例 1 输出

样例 2 输入

4 6

样例 2 输出

样例 3 输入

10 66

样例 3 输出

686029191

子任务

对于 $100\%$ 的数据，保证 $1\le n\le 10, 1\le k\le 10^5$。

测试点 $1,2$ 分别保证 $n=1,2$。
对于测试点 $i(3\le i\le 20)$，保证 $k\le 10^{(i+10)/6}$。

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