Ropes

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

There are $n$ ropes of lengths $a_i$. Ropes may be cut into pieces and leftovers may be discarded. Find the maximum real length $x$ such that at least $k$ pieces, each of length exactly $x$ can be obtained.

Input

The first line contains $n,k$. The next $n$ lines contain $a_i$.

Output

Print the maximum length. The answer is accepted if its absolute or relative error does not exceed $10^{-6}$.

Subtasks

• Subtask 1 — 20%: $n=1$.
• Subtask 2 — 30%: $1\le n,k\le1000$.
• Subtask 3 — 50%: $1\le n,k\le10^4$, $1\le a_i\le10^7$.

Examples

Input

4 11
802
743
457
539

Output

200.5000000000

Explanation

At length $200.5$, the ropes yield $4+3+2+2=11$ pieces.