Two warehouses each keep a sorted (non-decreasing) log of shipment values: log A has n values and log B has m values. You must pick exactly one value from A and one value from B; among all such cross pairs, find the minimum possible absolute difference between the pair's sum and a target T.

Input format

Line 1: three integers n, m, and T. Line 2: n space-separated integers, sorted non-decreasing — log A. Line 3: m space-separated integers, sorted non-decreasing — log B.

Output format

A single integer: the minimum value of |a + b - T| over all a in A and b in B.

Constraints

• 1 ≤ n, m ≤ 100000
• -1000000000 ≤ each value, T ≤ 1000000000
• Both logs are individually sorted in non-decreasing order.

3 3 10
1 4 6
2 5 9

0

2 2 0
-5 3
-2 4

1