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$, \displaystyle \min_{ 1\leq i\leq N}\displaystyle\min_{1\leq j\leq M} \lvert A_i-B_j\rvert$.

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.

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.

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

见题面 Input 部分

见题面 Output 部分