Takahashi has a playlist with $N$ songs. Song $i$ $(1 \leq i \leq N)$ lasts $T_i$ seconds.  
Takahashi has started random play of the playlist at time $0$.

Random play repeats the following: choose one song from the $N$ songs with equal probability and play that song to the end. Here, songs are played continuously: once a song ends, the next chosen song starts immediately. The same song can be chosen consecutively.

Find the probability that song $1$ is being played $(X + 0.5)$ seconds after time $0$, modulo $998244353$.

How to print a probability modulo $998244353$

It can be proved that the probability to be found in this problem is always a rational number. Also, the constraints of this problem guarantee that when the probability to be found is expressed as an irreducible fraction $\frac{y}{x}$, $x$ is not divisible by $998244353$.

Then, there is a unique integer $z$ between $0$ and $998244352$, inclusive, such that $xz \equiv y \pmod{998244353}$. Report this $z$.

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

```
$N$ $X$
$T_1$ $T_2$ $\ldots$ $T_N$
```

Print the probability, modulo $998244353$, that the first song in the playlist is being played $(X+0.5)$ seconds after time $0$.

-   $2 \leq N\leq 10^3$
-   $0 \leq X\leq 10^4$
-   $1 \leq T_i\leq 10^4$
-   All input values are integers.

369720131

Song 1 will be playing 6.5 seconds after time 0 if songs are played in one of the following orders.

• Song 1 → Song 1 → Song 1
• Song 2 → Song 1
• Song 3 → Song 1

The probability that one of these occurs is $\frac{7}{27}$.
We have $369720131×27≡7(\bmod\ {998244353})$, so you should print 369720131.

598946612

0.5 seconds after time 0, the first song to be played is still playing, so the sought probability is $\frac{1}{5}$.
Note that different songs may have the same length.