Wooden Board

$N$ trees are planted in a straight line, each $1$ unit apart.

On day $0$, every tree has height $0$. Each tree has width $1$. At the start of each day, the $i$-th tree grows by $1$ compared to the previous day with probability $p_i$ percent. Otherwise, it keeps the same height as the previous day.

You want to cut the largest rectangular region covered by the $N$ trees to get a large wooden board. The two sides of the board must be parallel to the ground.

For example, when 5 trees are planted and their heights are 1, 4, 2, 5, 3 in order, the board size is 8.

Find the expected area of the wooden board you can obtain on day $M$. See the Output section for the output format.

The first line contains the number of trees $N$ and the number of days $M$. $(1 \leq N, M \leq 30)$

The second line contains the growth percentages $p_1, p_2, \cdots, p_N$ of each tree per day. $(1 \leq p_i \leq 100)$

All input values are guaranteed to be integers.

The expected area is a rational number. When it is written as an irreducible fraction $\frac{y}{x}$, $x$ is guaranteed not to be a multiple of $998\,244\,353$. Then there is exactly one integer $0 \leq z < 998\,244\,353$ such that $xz \equiv y \pmod{998\,244\,353}$. Print this $z$.