21104번 - Miner 다국어

There are $n$ different minerals in a mine cave. The mine cave can be regarded as a coordinate axis, and the $i$-th mineral can be mined from any position in range $[l_i, r_i]$.

You are a miner in this mine cave. On each day, the foreman gives you a task of mining minerals. A task is a non-empty set of different minerals (there are $2^n - 1$ different tasks), and your goal is to collect all minerals in this set.

There are $m$ safe positions $a_i$ in the mine cave. A task is easy if and only if you can select a safe position $a_p$ and find all required minerals there.

Now, you want to count the number of easy tasks.

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 10^5$).

Then $n$ lines follow. Each of them contains two integers $l_i$ and $r_i$ ($1 \le l_i \le r_i \le 10^9$).

Then $m$ lines follow. Each of them contains a single integer $a_i$ ($1 \le a_i \le 10^9$).

Output a single line with a single integer: the number of easy tasks modulo $998\,244\,353$.