Santa Claus and Tangerines

题意翻译

### 题目描述 ​ 圣诞老人有n个橘子，每个橘子的第i个都是由 $a_{i}$片。圣诞老人来到一所有$k$个学生的学校。圣诞老人决定用橘子招待他们。 ​ 然而，橘子可能太少，不能给每个学生提供至少一个橘子。所以圣诞老人决定把橘子分成几个部分，这样就不会有人生气了。为了做到这一点，他可以把一个橘子或任何现存的部分分成两个更小的相等的部分。如果他想分割的部分的橘子瓣数量是奇数，那么得到的一个部分将比另一个多出一片。只由一片组成的橘子是不允许分割的。 ​ 圣诞老人想要送给每个人一个完整的橘子或者恰好是其中的一部分(这也意味着每个人都必须得到一个正数片)。一个或几个橘子或他们的部分可能留在圣诞老人那里没有分发。 ​ 若$b_{i}$为第i个学生最后的切片数,则圣诞老人的快乐值成为 $b_{i}$ 中最小的。 ​ 你的任务是在圣诞老人用橘子(或其中几瓣)招待每个人之后，求最大的快乐值。 ### 输入格式 ​ 第一行： 两个正整数 $n,k ( 1<=n<=10^{6} , 1<=k<=2·10^{9}) $ ​ 第二行： $n$个正整数，第$i$个数字表示$a_{i}$,即$i$个橘子有多少瓣，$( 1<=a_{i}<=10^{7})$ ### 输出格式 ​ 若无解输出-1，否则输出最大快乐值。

题目描述

Santa Claus has $ n $ tangerines, and the $ i $ -th of them consists of exactly $ a_{i} $ slices. Santa Claus came to a school which has $ k $ pupils. Santa decided to treat them with tangerines. However, there can be too few tangerines to present at least one tangerine to each pupil. So Santa decided to divide tangerines into parts so that no one will be offended. In order to do this, he can divide a tangerine or any existing part into two smaller equal parts. If the number of slices in the part he wants to split is odd, then one of the resulting parts will have one slice more than the other. It's forbidden to divide a part consisting of only one slice. Santa Claus wants to present to everyone either a whole tangerine or exactly one part of it (that also means that everyone must get a positive number of slices). One or several tangerines or their parts may stay with Santa. Let $ b_{i} $ be the number of slices the $ i $ -th pupil has in the end. Let Santa's joy be the minimum among all $ b_{i} $ 's. Your task is to find the maximum possible joy Santa can have after he treats everyone with tangerines (or their parts).

输入输出格式

输入格式

The first line contains two positive integers $ n $ and $ k $ ( $ 1<=n<=10^{6} $ , $ 1<=k<=2·10^{9} $ ) denoting the number of tangerines and the number of pupils, respectively. The second line consists of $ n $ positive integers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=10^{7} $ ), where $ a_{i} $ stands for the number of slices the $ i $ -th tangerine consists of.

输出格式

If there's no way to present a tangerine or a part of tangerine to everyone, print -1. Otherwise, print the maximum possible joy that Santa can have.

输入输出样例

输入样例 #1

3 2
5 9 3

输出样例 #1

5

输入样例 #2

2 4
12 14

输出样例 #2

6

输入样例 #3

2 3
1 1

输出样例 #3

-1

说明

In the first example Santa should divide the second tangerine into two parts with $ 5 $ and $ 4 $ slices. After that he can present the part with $ 5 $ slices to the first pupil and the whole first tangerine (with $ 5 $ slices, too) to the second pupil. In the second example Santa should divide both tangerines, so that he'll be able to present two parts with $ 6 $ slices and two parts with $ 7 $ slices. In the third example Santa Claus can't present $ 2 $ slices to $ 3 $ pupils in such a way that everyone will have anything.