Problem2673--Two Sets

2673: Two Sets

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
[Submit] [Status] [Web Board] [Creator:]

Description

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.

Source/Category

 
[Submit] [Status]