No.67 A Common Stick-Cutting Problem (1)

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No.67 A Common Stick-Cutting Problem (1)

レベル : / AI推定難易度 : 850 / 実行時間制限 : 1ケース 5.000秒 / メモリ制限 : 512 MB / 小数誤差許容問題　絶対誤差または相対誤差が $10^{-9}$ 以下。ただし、ジャッジ側の都合で500桁未満にしてください
タグ : （AC するまで非表示） / 解いたユーザー数 338
作問者 :

LayCurse

お気に入りにしたユーザー ProblemId : 145 / 自分の提出

問題文最終更新日: 2026-06-25 02:59:59

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yukicoder contest 53 (順位表) の他の問題:

Problem Statement

Yuki has $N$ sticks, and the length of the $i$-th stick is $L_i$.
The sticks can be cut freely (in the direction that divides their length), but they cannot be joined together.
Yuki wants to make $K$ sticks of the same length.
Write a program that finds the maximum possible length of the $K$ sticks that can be made.

Input

\(N\)
\(L_1\ L_2\ \cdots\ L_N\)
\(K\)

All inputs are given as integers.
$1 \leq N \leq 200000 = 2 \times 10^5$
$1 \leq L_i \leq 1000000000 = 10^9$
$1 \leq K \leq 10000000000 = 10^{10}$

Output

Output the maximum possible length on $1$ line.
The answer is considered correct if the absolute error or the relative error is at most $10^{-9}$.
Print a newline at the end.

Sample

Sample 1

Input

2
10 20
3

Output

10.00

By cutting the stick of length $20$ exactly into $2$ equal parts, you get $3$ sticks of length $10$.

Sample 2

Input

2
10 20
4

Output

6.666666666666667

By cutting the stick of length $20$ into $3$ equal parts, and cutting the stick of length $10$ so that only a length of $20/3$ remains and discarding the rest, you get $4$ sticks of length $20/3$.

Sample 3

Input

5
99 88 77 66 55
1

Output

Sample 4

Input

5
99 88 77 66 55
10

Output

Sample 5

Input

5
99 88 77 66 55
100000

Output

0.003849923001540

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