CF-B. Find The Array（构造题笔记）

鼠人今天写了每日一题，有个数学题蛮有意思的，我们来看看吧（顺便水一篇博客）

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一、题目

CF-1463
B. Find The Array
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
You are given an array [a1,a2,…,an] such that 1≤ai≤109. Let S be the sum of all elements of the array a.

Let’s call an array b of n integers beautiful if:

1≤bi≤109 for each i from 1 to n;
for every pair of adjacent integers from the array (bi,bi+1), either bi divides bi+1, or bi+1 divides bi (or both);
2∑i=1n|ai−bi|≤S.
Your task is to find any beautiful array. It can be shown that at least one beautiful array always exists.

Input
The first line contains one integer t (1≤t≤1000) — the number of test cases.

Each test case consists of two lines. The first line contains one integer n (2≤n≤50).

The second line contains n integers a1,a2,…,an (1≤ai≤109).

Output
For each test case, print the beautiful array b1,b2,…,bn (1≤bi≤109) on a separate line. It can be shown that at least one beautiful array exists under these circumstances. If there are multiple answers, print any of them.

Example
input

4
5
1 2 3 4 5
2
4 6
2
1 1000000000
6
3 4 8 1 2 3

output

3 3 3 3 3
3 6
1 1000000000
4 4 8 1 3 3

不想读题看这里

知道你们不想看英文（我也不喜欢），我把题干大致解说一下。
现在给你一个数组a，里面有n个元素，元素之和是S，请你构造一个数组长度同为n的b数组，满足以下条件：
1.b数组内任意一个元素满足可以被数组两边的元素整除，或者整除数组两边的元素
2.从1遍历到n，满足|a[i]-b[i]|<=S/2(也就是b数组内的元素大概要在a附近，或者说，方差要小)

二、想法

我们看条件一，要满足“b数组内任意一个元素满足可以被数组两边的元素整除”这个条件，我们很容易想到1是万能的，所以我们只需要把a数组某些元素改成1就可以了
条件二要满足a，b方差够小，那其实我们只用把a数组内奇数位，偶数位分别相加对比，如果偶数位和大，就把奇数位改成1，如果奇数大则相反

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