AT_arc207_a [ARC207A] Affinity for Artifacts

Snuke the wizard has $ N $ magical lamps numbered $ 1 $ to $ N $ . The cost of the $ i $ -th lamp is $ a_i $ . Initially, none of the lamps are lit. Snuke has an integer value called MP, which is initially $ X $ . When Snuke lights a lamp with cost $ x $ , his MP decreases by $ x $ . Each time Snuke lights one lamp, the cost of all lamps with cost at least $ 1 $ decreases by $ 1 $ . There are $ N! $ possible orders to light the lamps. Find the number, modulo $ 998244353 $ , of such orders where MP never becomes negative.

The input is given from Standard Input in the following format: > $ N $ $ X $ $ a_1 $ $ a_2 $ $ \dots $ $ a_N $

Print the answer.

### Sample Explanation 1 We explain one order where MP never becomes negative. - First, light lamp $ 1 $ . MP decreases by $ 0 $ . - Next, light lamp $ 3 $ . MP decreases by $ 1 $ . - Finally, light lamp $ 2 $ . MP decreases by $ 0 $ . Note that the cost of a lamp never becomes negative. ### Sample Explanation 3 Do not forget to find the remainder modulo $ 998244353 $ . ### Constraints - $ 1 \le N \le 100 $ - $ 0 \le a_i \le 10^{9} $ - $ 0 \le X \le 10^9 $ - All input values are integers.