Identify the Feasibility

题号：NC295135
时间限制：C/C++/Rust/Pascal 2秒，其他语言4秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Recently, Colin has been learning the relationship between sets and bitmasks. We can use binary numbers (bitmasks) to represent sets, and if some bits are $1$ in the bitmask, then it means that the sets include the elements corresponding to the indices of these bits.

Now Colin has $n$ non-negative integers $a_1,a_2,\cdots,a_n$ and all these integers are less than $2^k$ . Now Colin tries to use the concept of bitmasks and sets to understand the relationship between these integers.

For a non-negative integer $x\in[0,2^k)$ , Colin defines that $a_i$ is fesible with $a_j$ under the augmentation of $x$ , if and only if the set corresponding to the bitmask $a_i+x$ is a subset of the set corresponding to the bitmask $a_j+x$ . Then Colin uses $f(x)$ to represent the number of all the pairs $(i,j)$ such that $a_i$ is feasible with $a_j$ under the augmentation of $x$ .

Now Colin would like to ask you to calculate the sum of all the $f(x)$ , modulo $998244353$ .

Formally, please calculate
$\bigg(\sum_{x=0}^{2^k-1} f(x)\bigg) \mod 998244353$

输入描述:

The first line contains two integers , representing the number of integers Colin has and all of these integers are less than .

The following line contains  integers .

输出描述:

Output a single integer, representing the answer.

示例1

输入

复制

2 2
2 0

输出

复制

说明

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