WiFi

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

There are $m$ houses on a straight street and at most $k$ wireless access points may be placed at arbitrary real positions. Minimize the maximum distance from any house to its nearest access point. Print the optimum with one decimal digit.

Input

The first line contains $k,m$. The next $m$ lines contain house addresses.

Output

Print the optimal radius with one decimal place.

Subtasks

• Subtask 1 — 20%: $m\le100$.
• Subtask 2 — 30%: $m\le5000$.
• Subtask 3 — 50%: $m\le10^5$, address $\le10^6$.

Example

Input

2 3
1
3
10

Output

1.0

Explanation

Access points at 2 and 10 achieve maximum distance 1.0.