Game with Cards

Description:

Input:

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.

Output:

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.

Sample Input:

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

Sample Output:

Yes
0 1 

Sample Input:

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

Sample Output:

No

Sample Input:

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

Sample Output:

Yes
1 0 0 1 0