AT_abc464_f [ABC464F] Random Vault Heist

Kowasugi Bank has $N$ safes. Safe $i$ contains $A_i$ yen. One day, a robber entered the bank. The robber repeats the following operation until the total amount stolen reaches at least $X$ yen: - Choose one safe uniformly at random from the safes not yet opened, open it, and steal all the money inside. Find the expected value, modulo $998244353$, of the total amount stolen by the robber. Definition of expected value modulo $998244353$: It can be proved that the expected value sought is always a rational number. Moreover, under the constraints of this problem, it can also be proved that when this value is expressed as an irreducible fraction $\frac{P}{Q}$, it satisfies $Q \not\equiv 0 \pmod{998244353}$. Therefore, there exists a unique integer $R$ satisfying $R \times Q \equiv P \pmod{998244353}$, $0 \le R < 998244353$. Find this $R$.

The input is given from Standard Input in the following format: > $ N $ $ X $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Output the answer.

### Sample Explanation 1 There are two choices for the first safe to open. If safe $ 1 $ is opened first, the robber also opens safe $ 2 $ , so the total amount stolen is $ 13 $ yen. If safe $ 2 $ is opened first, the total already reaches at least $ X $ yen at that point, so the total amount stolen is $ 10 $ yen. Thus, the expected value is $ \frac{13 + 10}{2} = \frac{23}{2} $ . ### Sample Explanation 2 Regardless of the order in which they are opened, the total amount stolen when two safes have been opened is $ 2 $ yen. Thus, the expected value is $ 2 $ . ### Constraints - $ 1 \le N \le 40 $ - $ 1 \le A_i \le 10^{16} $ - $ 1 \le X \le \sum_{i=1}^{N} A_i $ - All input values are integers.