Nasshitaka4692 has $n$ variables $a_1, \dots, a_n$, all initially $0$. He will perform $k$ rounds of operations. In each round, he chooses one variable uniformly at random and increments it by $1$. He wants to know the expected value of $\max \{a_1, \dots, a_n\}$. You only need to help him calculate the result of this expected value multiplied by $n^k$, modulo $998244353$.
Input
Input two positive integers $n, k$.
Output
Output a single number representing the answer.
Examples
Input 1
2 5
Output 1
110
Input 2
4 6
Output 2
11544
Input 3
10 66
Output 3
686029191
Subtasks
For $100\%$ of the data, it is guaranteed that $1 \le n \le 10$ and $1 \le k \le 10^5$.
- Test cases $1$ and $2$ guarantee $n=1$ and $n=2$ respectively.
- For test cases $i$ ($3 \le i \le 20$), it is guaranteed that $k \le 10^{(i+10)/6}$.