Problem:
Score : 800 points

Problem Statement

You are given integers N,\ A and B.
Determine if there exists a permutation (P_0,\ P_1,\ ...\ P_{2^N-1}) of (0,\ 1,\ ...\ 2^N-1) that satisfies all of the following conditions, and create one such permutation if it exists.

P_0=A

P_{2^N-1}=B

For all 0 \leq i < 2^N-1, the binary representations of P_i and P_{i+1} differ by exactly one bit.

Constraints

1 \leq N \leq 17

0 \leq A \leq 2^N-1

0 \leq B \leq 2^N-1

A \neq B

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

If there is no permutation that satisfies the conditions, print NO.

If there is such a permutation, print YES in the first line.
Then, print (P_0,\ P_1,\ ...\ P_{2^N-1}) in the second line, with spaces in between.
If there are multiple solutions, any of them is accepted.

Sample Input 1

2 1 3

Sample Output 1

YES
1 0 2 3

The binary representation of P=(1,0,2,3) is (01,00,10,11), where any two adjacent elements differ by exactly one bit.

Sample Input 2

3 2 1

Sample Output 2

NO

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		int A = int.Parse(str[1]);
		int B = int.Parse(str[2]);
		int c = 1;
		int ct0 = 0;
		int ct1 = 0;
		int ct1i = -1;
		int[] LNa = new int[N];
		int[] LNb = new int[N];
		for(var i=0;i<N;i++){
			int a1 = (A/c)%2;
			int b1 = (B/c)%2;
			LNa[i] = a1;
			LNb[i] = b1;
			if(Math.Abs(a1-b1)==1){
				ct1++;
				ct1i = i;
			} else {
				ct0++;
			}
			c *= 2;
		}
		if(ct1!=1){
			Console.WriteLine("NO");
		} else {
			Console.WriteLine("YES");
			int L = (int)Math.Pow(2,N);
			int Li = (int)Math.Pow(2,ct1i);
			int aL = (A/Li)%2*Li;
			int bL = (B/Li)%2*Li;
			int[] LN = new int[N];
			int cta = 0;
			for(var i=0;i<N;i++){
				if(i != ct1i){
					LN[i] = cta;
					cta++;
				} else {
					LN[i] = N-1;
				}
			}
			int[]ans = new int[L];
			for(var i=0;i<L;i++){
				int a = 0;
				c = 1;
				for(var j=0;j<N;j++){
					int c1 = (i/c)%4;
					if(c1==0 || c1==3){
						a += LNa[j] * c;
					} else {
						a += (LNa[j]+1)%2 * c;
					}
					c *= 2;
				}
				ans[i] = a;
			}
			Console.Write(ans[0]);
			for(var i=1;i<L;i++){
				Console.Write(" "+ans[i]);
			}
		}
	}
}