Problem Statement

You are given two sequences: $A=(A_1,A_2, \\ldots ,A_N)$ consisting of $N$ positive integers, and $B=(B_1, \\ldots ,B_M)$ consisting of $M$ positive integers.

Find the minimum difference of an element of $A$ and an element of $B$, that is, $\\displaystyle \\min_{ 1\\leq i\\leq N}\\displaystyle\\min_{1\\leq j\\leq M} \\lvert A_i-B_j\\rvert$.

Constraints

• $1 \\leq N,M \\leq 2\\times 10^5$
• $1 \\leq A_i \\leq 10^9$
• $1 \\leq B_i \\leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $A_1$ $A_2$ $\\ldots$ $A_N$ $B_1$ $B_2$ $\\ldots$ $B_M$

Output

Print the answer.

Sample Input 1

2 2
1 6
4 9

Sample Output 1

2

Here is the difference for each of the four pair of an element of $A$ and an element of $B$: $\\lvert 1-4\\rvert=3$, $\\lvert 1-9\\rvert=8$, $\\lvert 6-4\\rvert=2$, and $\\lvert 6-9\\rvert=3$. We should print the minimum of these values, or $2$.

Sample Input 2

1 1
10
10

Sample Output 2

0

Sample Input 3

6 8
82 76 82 82 71 70
17 39 67 2 45 35 22 24

Sample Output 3

3