Polycarp's Picture Gallery

题意翻译

Polycarp不仅喜欢拍照，还喜欢向朋友展示他的照片。在他的个人网站上，他最近安装了一个小部件，可以通过滚动选项显示$n$ 张照片。在每一时刻，小部件都会显示一张照片，并可以选择显示上一张/下一张。从第一张照片，你可以切换到第二张或第$n$张，从第二张照片，你可以切换到第一张或第三张，等等。因此，导航是在一个周期内进行的。 Polycarp的收藏包括$m$ 个相册，第$i$ 个相册包含一张$a_{i}$ 照片。Polycarp希望选择$n$ 张照片并将它们放到一个新的小部件上。为了让访客对观看照片感兴趣，他将发布照片，这样一个相册中的两张照片就不会相邻（每张照片正好有两个邻居，第一张照片的邻居是第二张，第$n$ 张照片）。 帮助Polycarp编译照片库。从他的收藏中选择$n$ 张照片，并按顺序排列，使一个相册中的两张照片不会一张接一张地出现。

题目描述

Polycarp loves not only to take pictures, but also to show his photos to friends. On his personal website he has recently installed a widget that can display $ n $ photos with the scroll option. At each moment of time the widget displays exactly one photograph with the option showing the previous/next one. From the first photo, you can switch to the second one or to the $ n $ -th one, from the second photo you can switch to the third one or to the first one, etc. Thus, navigation is performed in a cycle. Polycarp's collection consists of $ m $ photo albums, the $ i $ -th album contains $ a_{i} $ photos. Polycarp wants to choose $ n $ photos and put them on a new widget. To make watching the photos interesting to the visitors, he is going to post pictures so that no two photos from one album were neighboring (each photo will have exactly two neighbors, the first photo's neighbors are the second and the $ n $ -th one). Help Polycarp compile a photo gallery. Select $ n $ photos from his collection and put them in such order that no two photos from one album went one after the other.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ m $ ( $ 3<=n<=1000 $ , $ 1<=m<=40 $ ), where $ n $ is the number of photos on the widget, and $ m $ is the number of albums. The second line contains $ m $ integers $ a_{1},a_{2},...,a_{m} $ ( $ 1<=a_{i}<=1000 $ ), where $ a_{i} $ is the number of photos in the $ i $ -th album.

输出格式

Print the single number -1 if there is no solution. Otherwise, print $ n $ numbers $ t_{1},t_{2},...,t_{n} $ , where $ t_{i} $ represents the number of the album of the $ i $ -th picture in the widget. The albums are numbered from 1 in the order of their appearance in the input. If there are several solutions, print any of them.

输入输出样例

输入样例 #1

4 3
1 3 5

输出样例 #1

3 1 3 2

输入样例 #2

10 2
5 5

输出样例 #2

2 1 2 1 2 1 2 1 2 1

输入样例 #3

10 3
1 10 3

输出样例 #3

-1