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EI2122Q1ADAM2 - Matching

Given the height of N men and M women. We need to form X pairs of one man and one woman. H is the maximum height difference of a pair, H = max({|pair.manHeight – pair.womanHeight| for X pairs}). What is the minimum possible value of H?

Input

-      The first line contains three integers N, M, X (1 ≤ N ≤ 105).

-      The second line contains N integers indicating the height of N men.

-      The third line contains M integers indicating the height of M women.

Output

The minimum possible value of H.

Note: 50% test case: X = N = M

 

Sample

Input

Output

5 6 3

150 180 165 184 156

152 168 175 159 168 190

3

5 5 5

150 180 165 184 156

152 168 175 159 168

12


Added by:Ha Minh Ngoc
Date:2021-11-15
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
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