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#F1905. Two Sets

    ID: 1911 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 6 上传者: 标签>2-SAT搜索并查集图匹配贪心图论数据结构算法思想提高难度共享题库Codeforces英文题面题目来源题面语言

Two Sets

题目描述

B. Two Sets
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 either 0, 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).

Examples
Input
4 5 9
2 3 4 5
Output
YES
0 0 1 1
Input
3 3 4
1 2 4
Output
NO
Note

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

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1481 题。保留原作者与原赛事署名。