Game with Cards

题意翻译

有两个数 $ a $ 和 $ b $ ，初始每个数都是 $ 0 $ 。你需要进行 $ n $ 次操作，并且数据保证所有操作所涉及的数值不超过 $ m $ 。 每次操作会有三行。对于第 $ i $ 次操作： 第一行是一个数 $ k_i (0 \le k_i \le m ) $ ，你需要用它去替换 $ a、b $ 中的任意一个，且仅一个。 第二行是两个数 $ a_{l,i} $ 和 $ b_{l,i} $ $ (0 \le a_{l,i} \le b_{l,i} \le m) $ ，需要满足操作后 $ a_{l,i} \le a \le b_{l,i} $ 。 第三行是两个数 $ a_{r,i} $ 和 $ b_{r,i} $ $ (0 \le a_{r,i} \le b_{r,i} \le m) $ ，需要满足操作后 $ a_{r,i} \le b \le b_{r,i} $ 。 问是否可以完成所有的 $ n $ 次操作。若可以输出 "Yes"，并在下一行依次输出每次操作是改的哪一个数， $ 0 $ 表示改的第一个数， $ 1 $ 表示改的第二个数。若不能则输出 "No"。有多种方案任意输出一种即可。 $ 2 \le n \le 10^5 ， 2 \le m \le 10^9 $ 。

题目描述

The Alice's computer is broken, so she can't play her favorite card game now. To help Alice, Bob wants to answer $ n $ her questions. Initially, Bob holds one card with number $ 0 $ in the left hand and one in the right hand. In the $ i $ -th question, Alice asks Bob to replace a card in the left or right hand with a card with number $ k_i $ (Bob chooses which of two cards he changes, Bob must replace exactly one card). After this action, Alice wants the numbers on the left and right cards to belong to given segments (segments for left and right cards can be different). Formally, let the number on the left card be $ x $ , and on the right card be $ y $ . Then after the $ i $ -th swap the following conditions must be satisfied: $ a_{l, i} \le x \le b_{l, i} $ , and $ a_{r, i} \le y \le b_{r,i} $ . Please determine if Bob can answer all requests. If it is possible, find a way to do it.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ m $ ( $ 2 \le n \le 100\,000 $ , $ 2 \le m \le 10^9 $ ) — the number of questions and the maximum possible value on the card. Then $ n $ queries are described. Every description contains 3 lines. The first line of the description of the $ i $ -th query contains a single integer $ k_i $ ( $ 0 \le k_i \le m $ ) — the number on a new card. The second line of the description of the $ i $ -th query contains two integers $ a_{l, i} $ and $ b_{l, i} $ ( $ 0 \le a_{l, i} \le b_{l, i} \le m $ ) — the minimum and maximum values of the card at the left hand after the replacement. The third line of the description of the $ i $ -th query contains two integers $ a_{r, i} $ and $ b_{r,i} $ ( $ 0 \le a_{r, i} \le b_{r,i} \le m $ ) — the minimum and maximum values of the card at the right hand after the replacement.

输出格式

At the first line, print "Yes", if Bob can answer all queries, and "No" otherwise. If Bob can answer all $ n $ queries, then at the second line print $ n $ numbers: a way to satisfy all requirements. If in $ i $ -th query Bob needs to replace the card in the left hand, print $ 0 $ , otherwise print $ 1 $ . If there are multiple answers, print any.

输入输出样例

输入样例 #1

2 10
3
0 3
0 2
2
0 4
0 2

输出样例 #1

Yes
0 1

输入样例 #2

2 10
3
0 3
0 2
2
3 4
0 1

输出样例 #2

No

输入样例 #3

5 10
3
0 3
0 3
7
4 7
1 3
2
2 3
3 7
8
1 8
1 8
6
1 6
7 10

输出样例 #3

Yes
1 0 0 1 0