Playlist

题意翻译

有多组测试数据。 有一个包含 $n$ 首歌的歌单，第 $i$ 首歌的风格为 $a_i$，现在循环播放该歌单（听完最后一首歌后回到第一首歌）。 设当前听完的歌 $B$ 风格为 $y$ ，上一首听完的歌 $A$ 风格为 $x$ 。 若 $\gcd{(x,y)=1}$ ，则删掉歌 $B$ ，从原歌单中 $B$ 的下一首歌 $C$ 开始听（此时不再考虑 $A$ 和 $C$ 风格的 $\gcd$ 的关系）。 请求出被删掉的歌以及删歌的顺序。 注：原题面中不存在 $A$ , $B$ , $C$ ，这里只是为了描述方便而引入。 数据范围：$1 \leqslant n \leqslant 10^5$，$1 \leqslant a_i \leqslant 10^9$ 。

题目描述

Arkady has a playlist that initially consists of $ n $ songs, numerated from $ 1 $ to $ n $ in the order they appear in the playlist. Arkady starts listening to the songs in the playlist one by one, starting from song $ 1 $ . The playlist is cycled, i. e. after listening to the last song, Arkady will continue listening from the beginning. Each song has a genre $ a_i $ , which is a positive integer. Let Arkady finish listening to a song with genre $ y $ , and the genre of the next-to-last listened song be $ x $ . If $ \operatorname{gcd}(x, y) = 1 $ , he deletes the last listened song (with genre $ y $ ) from the playlist. After that he continues listening normally, skipping the deleted songs, and forgetting about songs he listened to before. In other words, after he deletes a song, he can't delete the next song immediately. Here $ \operatorname{gcd}(x, y) $ denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers $ x $ and $ y $ . For example, if the initial songs' genres were $ [5, 9, 2, 10, 15] $ , then the playlist is converted as follows: \[5, 9, 2, 10, 15\] $ \to $ \[5, 9, 2, 10, 15\] $ \to $ \[5, 2, 10, 15\] (because $ \operatorname{gcd}(5, 9) = 1 $ ) $ \to $ \[5, 2, 10, 15\] $ \to $ \[5, 2, 10, 15\] $ \to $ \[5, 2, 10, 15\] $ \to $ \[5, 2, 10, 15\] $ \to $ \[5, 2, 10, 15\] $ \to $ \[5, 10, 15\] (because $ \operatorname{gcd}(5, 2) = 1 $ ) $ \to $ \[5, 10, 15\] $ \to $ \[5, 10, 15\] $ \to $ ... The bold numbers represent the two last played songs. Note that after a song is deleted, Arkady forgets that he listened to that and the previous songs. Given the initial playlist, please determine which songs are eventually deleted and the order these songs are deleted.

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10\,000 $ ). Description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 10^5 $ ) — the number of songs. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^9 $ ) — the genres of the songs. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

输出格式

For each test case, print a single line. First, print a single integer $ k $ — the number of deleted songs. After that print $ k $ distinct integers: deleted songs in the order of their deletion.

输入输出样例

输入样例 #1

5
5
5 9 2 10 15
6
1 2 4 2 4 2
2
1 2
1
1
1
2

输出样例 #1

2 2 3 
2 2 1 
2 2 1 
1 1 
0

说明

Explanation of the first test case is given in the statement. In the second test case, the playlist is converted as follows: \[1, 2, 4, 2, 4, 2\] $ \to $ \[1, 2, 4, 2, 4, 2\] $ \to $ \[1, 4, 2, 4, 2\] (because $ \operatorname{gcd}(1, 2) = 1 $ ) $ \to $ \[1, 4, 2, 4, 2\] $ \to $ \[1, 4, 2, 4, 2\] $ \to $ \[1, 4, 2, 4, 2\] $ \to $ \[1, 4, 2, 4, 2\] $ \to $ \[1, 4, 2, 4, 2\] $ \to $ \[4, 2, 4, 2\] (because $ \operatorname{gcd}(2, 1) = 1 $ ) $ \to $ \[4, 2, 4, 2\] $ \to $ ... In the third test case, the playlist is converted as follows: \[1, 2\] $ \to $ \[1, 2\] $ \to $ \[1\] (because $ \operatorname{gcd}(1, 2) = 1 $ ) $ \to $ \[1\] $ \to $ \[1\] (Arkady listened to the same song twice in a row) $ \to $ \[\] (because $ \operatorname{gcd}(1, 1) = 1 $ ). The fourth test case is same as the third after deletion of the second song. In the fifth test case, the same song is listened to over and over again, but since $ \operatorname{gcd}(2, 2) \ne 1 $ , it is not deleted.