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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace abc119d
{
    class Program
    {
        static void Main(string[] args)
        {
            var NAB = ReadIntList();
            var N = NAB[0];
            var L = (int)Math.Pow(2, N);
            var A = NAB[1];
            var B = NAB[2];

            var xor = A ^ B;
            var diff = 0;
            for (int i = 0; i < N; i++)
            {
                diff += (xor >> i) & 1;
            }
            if (diff % 2 == 1)
            {
                Console.WriteLine("YES");
                var ans = new int[L];
                for (int i = 0; i < L; i++)
                {
                    ans[i] = A;
                    xor = A ^ B;
                    if (xor == 0 || xor%2 == 1)
                    {
                        A ^= 1;
                    }
                    else
                    {
                        A ^= 1 << (int)Math.Log(xor,2);
                    }
                }
                Console.WriteLine(String.Join(" ", ans));
            }
            else
            {
                Console.WriteLine("NO");
            }
#if DEBUG
            Console.ReadKey();
#endif
        }

        private static bool IsRange(int a, int from, int to) => (from <= a && a <= to);
        private static int ReadInt() => int.Parse(Console.ReadLine());
        private static List<int> ReadIntList() => Console.ReadLine().Split().Select(int.Parse).ToList();
        private static double ReadDouble() => double.Parse(Console.ReadLine());
        private static List<double> ReadDoubleList() => Console.ReadLine().Split().Select(double.Parse).ToList();
        private static long ReadLong() => long.Parse(Console.ReadLine());
        private static List<long> ReadLongList() => Console.ReadLine().Split().Select(long.Parse).ToList();
        private static List<int> Int2Digits(int a) => a.ToString().ToCharArray().Select(_ => int.Parse(_.ToString())).ToList();
        private static int BinarySearch<Type>(IReadOnlyList<Type> s, Type target) // target 以下の最大要素のインデックスを返す
            where Type : IComparable
        {
            var lower = 0;
            var upper = s.Count - 1;
            while (upper - lower > 1)
            {
                var mid = lower + (upper - lower) / 2;
                if (s[mid].CompareTo(target) <= 0)
                {
                    lower = mid;
                }
                else
                {
                    upper = mid;
                }

            }
            return lower;
        }
    }
}