Power Sockets

题意翻译

- 初始给出 $n$ 条长度分别为 $l_1,l_2,\dots,l_n$ 的链，以及一棵只有一个根节点的树，所有点初始都为白色。 - 每次操作可以用一条边将一条链中的一个点 $u$ 和树上某个白点 $v$ 连接起来，$u,v$ 都变黑。一条链至多操作一次，也可以不操作。 - 操作完后树的权值为根节点到第 $k$ 近的白点的距离。问操作方案所得树中最小的权值。若无法得到 $k$ 个白点，则输出 $-1$。 - $1 \leq n \leq 2 \times 10^5,2 \leq k \leq 10^9,3 \le l_i \le 2 \times 10^5$

题目描述

// We decided to drop the legend about the power sockets but feel free to come up with your own :^) Define a chain: - a chain of length $ 1 $ is a single vertex; - a chain of length $ x $ is a chain of length $ x-1 $ with a new vertex connected to the end of it with a single edge. You are given $ n $ chains of lengths $ l_1, l_2, \dots, l_n $ . You plan to build a tree using some of them. - Each vertex of the tree is either white or black. - The tree initially only has a white root vertex. - All chains initially consist only of white vertices. - You can take one of the chains and connect any of its vertices to any white vertex of the tree with an edge. The chain becomes part of the tree. Both endpoints of this edge become black. - Each chain can be used no more than once. - Some chains can be left unused. The distance between two vertices of the tree is the number of edges on the shortest path between them. If there is at least $ k $ white vertices in the resulting tree, then the value of the tree is the distance between the root and the $ k $ -th closest white vertex. What's the minimum value of the tree you can obtain? If there is no way to build a tree with at least $ k $ white vertices, then print -1.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ k $ ( $ 1 \le n \le 2 \cdot 10^5 $ , $ 2 \le k \le 10^9 $ ) — the number of chains and the minimum number of white vertices a tree should have to have a value. The second line contains $ n $ integers $ l_1, l_2, \dots, l_n $ ( $ 3 \le l_i \le 2 \cdot 10^5 $ ) — the lengths of the chains.

输出格式

Print a single integer. If there is no way to build a tree with at least $ k $ white vertices, then print -1. Otherwise, print the minimum value the tree can have.

输入输出样例

输入样例 #1

1 2
3

输出样例 #1

2

输入样例 #2

3 3
4 3 3

输出样例 #2

3

输入样例 #3

3 5
4 3 4

输出样例 #3

4

输入样例 #4

2 10
5 7

输出样例 #4

-1

说明

You are allowed to not use all the chains, so it's optimal to only use chain of length $ 4 $ in the second example.