Counting Subsets with Product Greater Than m

You are given n integers \(a_1, a_2, \dots, a_n\) forming a multiset. A subset is defined by the indices of the elements you choose; two subsets are considered different if and only if the sets of indices they contain are different. The product of the elements in a subset is defined in the natural way, and by convention the product of the empty set is \(1\).

Your task is to count how many subsets have a product strictly greater than \(m\). Since the answer may be very large, output your answer modulo \(998244353\).

Mathematical Definition:

Find the number of subsets \(S\) such that \[ \prod_{i \in S} a_i > m, \quad \text{with } \prod_{i \in \emptyset} a_i = 1. \]

inputFormat

The first line contains two integers n and m — the number of elements and the threshold, respectively.

The second line contains n integers \(a_1, a_2, \dots, a_n\), which represent the elements of the multiset.

Constraints: It is guaranteed that n is small enough to allow iterating over all \(2^n\) subsets. All \(a_i\) and \(m\) are positive integers.

outputFormat

Output a single integer: the number of subsets whose product is greater than \(m\), taken modulo \(998244353\).

sample

3 2
1 2 3

4