WiFi

The residents of Main Street have decided to install wireless internet covering every house, and they need your help deciding where to place the wireless access points. They want the signal in every house to be as strong as possible, but their limited budget caps how many access points they can buy. They will place the access points so that the largest distance between any house and its nearest access point is as small as possible.

Main Street is a perfectly straight road. The street number of each house equals its distance, in metres, from the end of the street. For example, the house at 123 Main Street is exactly 123 metres from the end of the street. Access points may be placed at any point along the street.

The first line contains an integer: the number of test cases. Each test case begins with a line containing two positive integers $n$ and $m$ — the number of access points the residents can buy and the number of houses on Main Street. Each of the following $m$ lines contains one house number. There are at most 100,000 houses, and every house number is at most 1,000,000.

For each test case, output a single line with one number: the largest distance between any house and its nearest access point. Round this distance to the nearest tenth of a metre and print it with exactly one digit after the decimal point.