Problem Statement

You are given positive integers $N, M$.

For a positive integer $d$, define the repunit with $d$ digits as the integer $\displaystyle\sum_{i = 0}^{d - 1} 10^i$.

Find the number, modulo $998244353$, of integers that can be expressed as the sum of (not necessarily distinct) $N$ repunits, each with at least $1$ digit and at most $M$ digits.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq M \leq 10^9$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M

Output

Output the answer.