Description

Given two arrays $x[]$ and $y[]$ of lengths $n$ and $m$ respectively. Take any element $x[i]$ from $x$ and any element $y[j]$ from $y$, their absolute difference is $|x[i] - y[j]|$. There are $n × m$ such differences, and the minimum value among them is called the distance between the arrays.
Please write a program to find the distance between the arrays.

Input Format

The first line contains two integers $n$ and $m$ ($1≤n,m≤10^6$).
The next line contains $n$ integers representing array $x$.
The next line contains $m$ integers representing array $y$.
The absolute values of the array elements are less than or equal to $10^8$.

Output Format

Output a single integer representing the distance between the two arrays.

Sample

5 5
1 2 3 4 5
6 7 8 9 10

1