Zhang Fengxiang is a keyboardist who formed a band called "Ave Wujica" and performs under the stage name "oblivious." She wears a mask during performances, which (according to her) is to maintain the band's worldview.

After taking off the mask, Zhang Fengxiang is just a customer service representative working hard to save up for the band's next performance. There are $n$ days left until the next performance, and she needs to cover a funding gap of $a$ yuan. Since her customer service job is not very stable, her daily income is uniformly and randomly distributed in cents within the range $[0, 1]$ yuan. That is, she earns $0, 1, \dots, 100$ cents with a probability of $\frac{1}{101}$ each. She wants to know the probability that she will be able to cover the funding gap of $a$ yuan after working for $n$ days.

Input

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

Output

Output an integer representing the probability modulo $998244353$.

Constraints

$n, a \leq 300$

Examples

Input 1

2 1

Output 1

444762336

Input 2

262 198

Output 2

631217166

Note

Earning $1$ yuan a day—perhaps Teacher Sakiko should just quit this customer service job.