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: Runtime Error)

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];
		int[] D = new int[N];
		int[] ctL = new int[N];
		for(var i=0;i<N;i++){
			D[i] = c;
			int a1 = (A/c)%2;
			int b1 = (B/c)%2;
			LNa[i] = a1;
			LNb[i] = b1;
			if(Math.Abs(a1-b1)%2==1){
				ct1++;
				ctL[i]=1;
				ct1i = i;
			} else {
				ct0++;
			}
			c *= 2;
		}
		if(ct1%2==0){
			Console.WriteLine("NO");
		} else {
			Console.WriteLine("YES");
			List<int> ans = Ar(N,A,B);
			Console.Write(ans[0]);
			for(var i=1;i<ans.Count;i++){
				Console.Write(" "+ans[i]);
			}
		}
	}
	static List<int> Ar(int n,int a,int b){
		int L = (int)Math.Pow(2,n);		
		List<int> A = new List<int>();
		if(n==1){
			A.Add(a);
			A.Add(b);
		} else {
			int c = 1;
			for(var i=0;i<n;i++){
				int a1 = a/c%2;
				int b1 = b/c%2;
				if(a1!=b1){
					int a2 = a%c+a/(c*2)*c;
					int b2 = b%c+b/(c*2)*c;
					int a3 = (a2+1)%2;
					A.AddRange(Ar(n-1,a2,a3));
					for(var j=0;j<L/2;j++){
						int a4 = A[j]/c;
						A[j] = a4*2*c+a1*c+A[j]%c;
					}
					A.AddRange(Ar(n-1,a3,b2));
					for(var j=L/2;j<L;j++){
						int a4 = A[j]/c;
						A[j] = a4*2*c+b1*c+A[j]%c;
					}
					break;
				} else {
					c *= 2;
				}
			}
		}
		return A;
	}
}