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.Diagnostics;
using System.IO;
using System.Linq;

internal class C {
    static void Main() => CustomMain();

    static void Solve() {
        int n, a, b;
        ReadMulti(out n, out a, out b);

        var bit = BitCount(a ^ b);
        if (IsEven(bit)) {
            WriteAnswer("NO");
            return;
        }

        WriteAnswer("YES");
        int size = (int) Math.Pow(2, n);
        var p = new int[size];
        p[0] = a;
        p[size - 1] = b;
        for (int i = 1; i < size - 1; i++) {
            if (p[i - 1] == b) {
                for (int j = 0; j < n; j++) {
                    var m = 1 << j;
                    if ((p[i - 1] & m) != 0) {
                        p[i] = p[i - 1] ^ m;
                        break;
                    }
                }
            } else {
                var d = p[i - 1] ^ b;
                for (int j = 0; j < n; j++) {
                    var m = 1 << j;
                    if ((d & m) != 0) {
                        p[i] = p[i - 1] | m;
                        break;
                    }
                }
            }
        }

        WriteAnswer(string.Join(" ", p));
    }

    static int BitCount(int n) {
        int cnt = 0;
        for (uint mask = 1; mask != 0; mask <<= 1) {
            if ((n & mask) != 0)
                ++cnt;
        }

        return cnt;
    }


    static void CustomMain() {
#if DEBUG
        // ファイルからテストケースを読み込む
        ChangeStdIn();
        // 時間計測
        var stopwatch = new Stopwatch();
        stopwatch.Start();
#endif
        // 出力高速化
        var streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
        Console.SetOut(streamWriter);
        // 回答
        Solve();
#if DEBUG
        stopwatch.Stop();
        Console.WriteLine(stopwatch.Elapsed);
#endif
        Console.Out.Flush();
    }

    static string ReadString() => Console.ReadLine().Trim();
    static int ReadInt() => int.Parse(ReadString());
    static long ReadLong() => long.Parse(ReadString());
    static float ReadFloat() => float.Parse(ReadString());
    static double ReadDouble => double.Parse(ReadString());

    static string[] ReadStringArray() => ReadString().Split(' ');
    static int[] ReadIntArray() => Array.ConvertAll(ReadString().Split(' '), int.Parse);
    static long[] ReadLongArray() => Array.ConvertAll(ReadString().Split(' '), long.Parse);
    static float[] ReadFloatArray() => Array.ConvertAll(ReadString().Split(' '), float.Parse);
    static double[] ReadDoubleArray() => Array.ConvertAll(ReadString().Split(' '), double.Parse);

    static T TypeConversion<T>(string s) {
        if (typeof(T) == typeof(int)) {
            return (T) Convert.ChangeType(int.Parse(s), typeof(T));
        } else if (typeof(T) == typeof(long)) {
            return (T) Convert.ChangeType(long.Parse(s), typeof(T));
        } else if (typeof(T) == typeof(double)) {
            return (T) Convert.ChangeType(double.Parse(s), typeof(T));
        } else {
            return (T) Convert.ChangeType(s, typeof(T));
        }
    }

    static void ReadMulti<T, U>(out T a, out U b) {
        var str = ReadStringArray();
        a = TypeConversion<T>(str[0]);
        b = TypeConversion<U>(str[1]);
    }

    static void ReadMulti<T, U, V>(out T a, out U b, out V c) {
        var str = ReadStringArray();
        a = TypeConversion<T>(str[0]);
        b = TypeConversion<U>(str[1]);
        c = TypeConversion<V>(str[2]);
    }

    static void WriteAnswer(object ans) => Console.WriteLine(ans);

    static bool IsOdd(long num) {
        return (num & 1) == 1;
    }

    static bool IsEven(long num) {
        return (num & 1) == 0;
    }

    static long GCD(long a, long b) {
        return b != 0 ? GCD(b, a % b) : a;
    }

    static long RoundUp(long a, long b) {
        return (a + b - 1) / b;
    }


    static void ChangeStdIn() {
        var path = "./../../TestCase.txt";
        var exStdIn = new System.IO.StreamReader(path);
        Console.SetIn(exStdIn);
    }
}