【cf468B】Two Sets

2014年9月21日1,2380

Little X has n distinct integers: p1, p2, …, pn. He wants to divide all of them into two sets A and B. The following two conditions must be satisfied:

  • If number x belongs to set A, then number a - x must also belong to set A.
  • If number x belongs to set B, then number b - x must also belong to set B.

Help Little X divide the numbers into two sets or determine that it’s impossible.

Input

The first line contains three space-separated integers n, a, b (1 ≤ n ≤ 105; 1 ≤ a, b ≤ 109). The next line contains n space-separated distinct integers p1, p2, …, pn (1 ≤ pi ≤ 109).

Output

If there is a way to divide the numbers into two sets, then print “YES” in the first line. Then print n integers: b1, b2, …, bn (bi equals either0, or 1), describing the division. If bi equals to 0, then pi belongs to set A, otherwise it belongs to set B.

If it’s impossible, print “NO” (without the quotes).

Sample test(s)
input

output

input

output

Note

It’s OK if all the numbers are in the same set, and the other one is empty.

 

为什么你们都会做。。。

我的思路完全偏了。。。

可以先确定一个数在某个集合,然后可以确定一系列和它相关的数所在集合,看是否矛盾

具体用dfs来搞

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