Bridge

Two rivers flow through a city from north to south, and houses stand in a row along each river, as in the picture. To let the people living on both banks reach the other side faster, we want to build a single bridge connecting the two rivers.

The left river is exactly the vertical line $x = -1$, and the right river is exactly the vertical line $x = 1$. A bridge is drawn as a segment parallel to the $x$-axis that connects one point on each river. Each house is a point on one of the vertical lines.

The left houses are at $(-1, a_i)$ ($i = 1, \dots, n$) and the right houses are at $(1, b_j)$ ($j = 1, \dots, m$). If the bridge is placed at height $h$ (that is, it connects the points $(-1, h)$ and $(1, h)$), the distance from a left house $a_i$ across the bridge to a right house $b_j$ is $|a_i - h| + 2 + |h - b_j|$.

Write a program that finds the bridge height $h$ minimizing the sum of these distances over all (left house, right house) pairs:

$\sum_{i,j} d(a_i, b_j) = \sum_{i,j} \left( |a_i - h| + 2 + |h - b_j| \right)$

The first line contains the number of test cases $T$.

The first line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 10^6$), where $n$ is the number of houses on the left river and $m$ is the number of houses on the right river. The next $n$ lines each contain a left house position $a_i$, and the following $m$ lines each contain a right house position $b_j$ ($|a_i|, |b_j| \le 10^7$). All positions are integers.

For each test case, print on its own line the height $h$ that minimizes the sum of distances, rounded to one decimal place. If several such $h$ exist, print the smallest one.