Little Z is a pigeon keeper. One day, Little Z feeds corn to his pigeons. There are $n$ pigeons in total, and every second, Little Z chooses one pigeon with equal probability and gives it one grain of corn. A pigeon is full if and only if the number of corn grains it has eaten is $\ge k$.

Little Z wants you to tell him the expected number of seconds until all pigeons are full.

Assuming the answer in its simplest fractional form is $\frac{a}{b}$, you need to find $w$ such that $a \equiv b \cdot w \pmod{998244353} \; (0 \le w < 998244353)$.

Note: To help contestants verify the correctness of their programs, the provided files include the source code of a simulator, which contestants should compile themselves. This simulator will repeatedly simulate the process described in the problem indefinitely and output the average number of seconds per simulation as a real number. The simulator guarantees an accuracy of $3 \sim 4$ significant digits.

Input

A single line containing two positive integers $n$ and $k$.

Output

A single line containing the answer.

Examples

Input 1

1 1

Output 1

1

Subtasks

This problem is evaluated using subtasks.

Subtask 1 ($4pts$): $n = 1$.

Subtask 2 ($11pts$): $k = 1$.

Subtask 3 ($19pts$): $k = 2$.

Subtask 4 ($46pts$): $k \le 50$.

Subtask 5 ($20pts$): No special constraints.

For all data, $n \le 50$ and $k \le 1000$.