A10975 | Office Keys

There are $n$ people and $k$ keys on a straight line. Every person wants to get to the office which is located on the line as well. To do that, he needs to reach some point with a key, take the key and then go to the office. Once a key is taken by somebody, it couldn't be taken by anybody else.

You are to determine the minimum time needed for all $n$ people to get to the office with keys. Assume that people move a unit distance per $1$ second. If two people reach a key at the same time, only one of them can take the key. A person can pass through a point with a key without taking it.

The first line contains three integers $n$ , $k$ and $p$ ( $1<=n<=1000$ , $n<=k<=2000$ , $1<=p<=10^{9}$ ) — the number of people, the number of keys and the office location.

The second line contains $n$ distinct integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{9}$ ) — positions in which people are located initially. The positions are given in arbitrary order.

The third line contains $k$ distinct integers $b_{1},b_{2},...,b_{k}$ ( $1<=b_{j}<=10^{9}$ ) — positions of the keys. The positions are given in arbitrary order.

Note that there can't be more than one person or more than one key in the same point. A person and a key can be located in the same point.

Print the minimum time (in seconds) needed for all $n$ to reach the office with keys.