A16359 | I Wanna be the Team Leader

Monocarp is a team leader in a massive IT company.

There are $m$ projects his team of programmers has to complete, numbered from $1$ to $m$ . The $i$ -th project has a difficulty level $b_i$ .

There are $n$ programmers in the team, numbered from $1$ to $n$ . The $j$ -th programmer has a stress tolerance level $a_j$ .

Monocarp wants to assign the programmers to the projects in such a way that:

- each programmer is assigned to no more than one project;
- each project has at least one programmer assigned to it;
- let $k$ programmers be assigned to the $i$ -th project; then all the assigned programmers have to have a stress tolerance level greater than or equal to $\frac{b_i}{k}$ .

Help Monocarp to find a valid assignment. If there are multiple answers, print any of them.

The first line contains two integers $n$ and $m$ ( $1 \le n \le 2 \cdot 10^5$ ; $1 \le m \le 20$ ) — the number of programmers and the number of projects.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ ) — the stress tolerance level of each programmer.

The third line contains $m$ integers $b_1, b_2, \dots, b_m$ ( $1 \le b_i \le 10^9$ ) — the difficulty level of each project.

If there is no valid assignment, print "NO".

Otherwise, in the first line, print "YES". In the $i$ -th of the next $m$ lines, print the list of the programmers assigned to the $i$ -th project: first, the number of programmers, then their indices in an arbitrary order.

If there are multiple answers, print any of them.