Problem Description

Given $n$ integers $a_1\sim a_n$, in the multiset formed by them, how many subsets have a product of elements greater than $m$? (The product of elements of the empty set is equal to $1$.)

Two subsets are different if and only if the indices of the elements they contain are different.

The answer is very large, so please output its value modulo $998244353$.

Input Format

The first line contains two integers $n, m$.

The next line contains $n$ positive integers $a_1\sim a_n$, describing this multiset.

Output Format

Output one integer in one line, which is the answer modulo $998244353$.

4 4
1 1 2 3

4

20 123456
1 5 12 24 189893 233333 2 22 134 3284 28456 261 50 10 1 2 2 2 2 22

1036360

Hint

[Sample $1$ Explanation]

The following subsets satisfy the requirement: $\{a_3,a_4\}$, $\{a_1,a_3,a_4\}$, $\{a_2,a_3,a_4\}$, $\{a_1,a_2,a_3,a_4\}$.

[Constraints]

For all testdata, $0\le n,m\le 10^6$, $1\le a_i\le 10^6$.

The detailed constraints are shown in the table below:

Translated by ChatGPT 5