Problem Statement

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.

Input

The input is given from Standard Input in the following format:
N X
$T_1 T_2 \ldots T_N$

Output

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

Constraints

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

Sample Input 1

3 6
3 5 6

Sample Output 1

369720131

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

• Song $1 \to$ Song $1 \to$ Song 1
• Song $2 \to$ Song 1
• Song $3 \to$ Song 1

The probability that one of these occurs is $\frac{7}{27}$.
We have $369720131\times 27\equiv 7 \pmod{998244353}$, so you should print 369720131.

Sample Input 2

5 0
1 2 1 2 1

Sample Output 2

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.

Sample Input 3

5 10000
1 2 3 4 5

Sample Output 3

586965467

见题面 Input 部分

见题面 Output 部分