Generating Sets

题意翻译

题目大意：给出一个 $set$，是 $setY$，由 $n$ 个不同的正整数 $y[i]$ 组成；$setX$由 $n$ 个不同的正整数 $x[i]$ 组成，现在可以对任意 $x[i]$ 进行多个以下操作： 1. $x[i] = 2 * x[i]$ 2. $x[i] = 2 * x[i] + 1$ 如果经过操作后的 $setX$ 和 $setY$ 是相同的，认为 $setX$ 能生成 $setY$。（按照从大到小的排序后，一一对应） 现在给出 $n$ 个数字 $y[i]$，求出 $setX$，要求 $setX$ 的最大数字最小（如果有多个答案，输出任意一个） $1 ≤ y[i] ≤ 1e9,n = 5w$ by [guyugeng2007](https://www.luogu.com.cn/user/554872)

题目描述

You are given a set $ Y $ of $ n $ distinct positive integers $ y_{1},y_{2},...,y_{n} $ . Set $ X $ of $ n $ distinct positive integers $ x_{1},x_{2},...,x_{n} $ is said to generate set $ Y $ if one can transform $ X $ to $ Y $ by applying some number of the following two operation to integers in $ X $ : 1. Take any integer $ x_{i} $ and multiply it by two, i.e. replace $ x_{i} $ with $ 2·x_{i} $ . 2. Take any integer $ x_{i} $ , multiply it by two and add one, i.e. replace $ x_{i} $ with $ 2·x_{i}+1 $ . Note that integers in $ X $ are not required to be distinct after each operation. Two sets of distinct integers $ X $ and $ Y $ are equal if they are equal as sets. In other words, if we write elements of the sets in the array in the increasing order, these arrays would be equal. Note, that any set of integers (or its permutation) generates itself. You are given a set $ Y $ and have to find a set $ X $ that generates $ Y $ and the maximum element of $ X $ is mininum possible.

输入输出格式

输入格式

The first line of the input contains a single integer $ n $ ( $ 1<=n<=50000 $ ) — the number of elements in $ Y $ . The second line contains $ n $ integers $ y_{1},...,y_{n} $ ( $ 1<=y_{i}<=10^{9} $ ), that are guaranteed to be distinct.

输出格式

Print $ n $ integers — set of distinct integers that generate $ Y $ and the maximum element of which is minimum possible. If there are several such sets, print any of them.

输入输出样例

输入样例 #1

5
1 2 3 4 5

输出样例 #1

4 5 2 3 1 

输入样例 #2

6
15 14 3 13 1 12

输出样例 #2

12 13 14 7 3 1 

输入样例 #3

6
9 7 13 17 5 11

输出样例 #3

4 5 2 6 3 1 

题意翻译

题目大意：给出一个 $set$，是 $setY$，由 $n$ 个不同的正整数 $y[i]$ 组成；$setX$由 $n$ 个不同的正整数 $x[i]$ 组成，现在可以对任意 $x[i]$ 进行多个以下操作： 1. $x[i] = 2 * x[i]$ 2. $x[i] = 2 * x[i] + 1$ 如果经过操作后的 $setX$ 和 $setY$ 是相同的，认为 $setX$ 能生成 $setY$。（按照从大到小的排序后，一一对应） 现在给出 $n$ 个数字 $y[i]$，求出 $setX$，要求 $setX$ 的最大数字最小（如果有多个答案，输出任意一个） $1 ≤ y[i] ≤ 1e9,n = 5w$ by [guyugeng2007](https://www.luogu.com.cn/user/554872)