CF1408D.Searchlights

There are $n$ robbers at coordinates $(a_1, b_1)$ , $(a_2, b_2)$ , ..., $(a_n, b_n)$ and $m$ searchlight at coordinates $(c_1, d_1)$ , $(c_2, d_2)$ , ..., $(c_m, d_m)$ .

In one move you can move each robber to the right (increase $a_i$ of each robber by one) or move each robber up (increase $b_i$ of each robber by one). Note that you should either increase all $a_i$ or all $b_i$ , you can't increase $a_i$ for some points and $b_i$ for some other points.

Searchlight $j$ can see a robber $i$ if $a_i \leq c_j$ and $b_i \leq d_j$ .

A configuration of robbers is safe if no searchlight can see a robber (i.e. if there is no pair $i,j$ such that searchlight $j$ can see a robber $i$ ).

What is the minimum number of moves you need to perform to reach a safe configuration?

The first line of input contains two integers $n$ and $m$ ( $1 \leq n, m \leq 2000$ ): the number of robbers and the number of searchlight.

Each of the next $n$ lines contains two integers $a_i$ , $b_i$ ( $0 \leq a_i, b_i \leq 10^6$ ), coordinates of robbers.

Each of the next $m$ lines contains two integers $c_i$ , $d_i$ ( $0 \leq c_i, d_i \leq 10^6$ ), coordinates of searchlights.

Print one integer: the minimum number of moves you need to perform to reach a safe configuration.

In the first test, you can move each robber to the right three times. After that there will be one robber in the coordinates $(3, 0)$ .

The configuration of the robbers is safe, because the only searchlight can't see the robber, because it is in the coordinates $(2, 3)$ and $3 > 2$ .

In the second test, you can move each robber to the right two times and two times up. After that robbers will be in the coordinates $(3, 8)$ , $(8, 3)$ .

It's easy the see that the configuration of the robbers is safe.

It can be proved that you can't reach a safe configuration using no more than $3$ moves.