AT_abc436_g [ABC436G] Linear Inequation

You are given a length- $ N $ sequence of positive integers $ A=(A _ 1,A _ 2,\ldots,A _ N) $ and a positive integer $ M $ . Find the number of length- $ N $ sequences of non-negative integers $ x=(x _ 1,x _ 2,\ldots,x _ N) $ that satisfy the following condition: - $ \displaystyle\sum _ {i=1} ^ NA _ ix _ i\le M $ The number can be very large, so find it modulo $ 998244353 $ .

The input is given from Standard Input in the following format: > $ N $ $ M $ $ A _ 1 $ $ A _ 2 $ $ \ldots $ $ A _ N $

Print the number, modulo $ 998244353 $ , of non-negative integer sequences that satisfy the condition.

### Sample Explanation 1 The sequences $ x $ that satisfy the condition are the following $ 10 $ : $ (0,0,0,0),(0,0,0,1),(0,0,0,2),(0,0,0,3),(0,0,1,0),(0,0,1,1),(0,0,2,0),(0,1,0,0),(0,1,0,1),(1,0,0,0) $ . Thus, print `10`. ### Sample Explanation 3 There are $ 1000000008 $ sequences $ x $ that satisfy the condition. Print this modulo $ 998244353 $ , which is $ 1755655 $ . ### Constraints - $ 1\le N\le100 $ - $ 1\le A _ i\le100\ (1\le i\le N) $ - $ 1\le M\le10 ^ {18} $ - All input values are integers.