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;

public class CSharp{
    public static void Main(){
        Kyopuro chokudai = new Kyopuro();
	    chokudai.AtCoder();
	}
}

public class Kyopuro{
    public void AtCoder(){
        string[] s = Console.ReadLine().Split(' ');
        int n = int.Parse(s[0]);
        int a = int.Parse(s[1]);
        int b = int.Parse(s[2]);
        int x = 0;
        int y = 0;
        int ta = a;
        int tb = b;
        for(int i=0; i<n; i++){
            if(ta % 2 == 1) x++;
            if(tb % 2 == 1) y++;
            ta /= 2;
            tb /= 2;
        }
        if(x % 2 == y % 2){
            Console.WriteLine("NO");
            return;
        }
        Console.WriteLine("YES");
        int[] t = new int[n+1];
        t[0] = 1;
        for(int i=1; i<=n; i++){
            t[i] = t[i-1] * 2;
        }
        
        int[] z = new int[t[n]];
        z[0] = 0;
        z[1] = 1;
        for(int i=1; i<n; i++){
            for(int j=t[i]; j<t[i+1]; j++){
                z[j] = z[t[i+1] - j - 1];
                z[j] += t[i];
            }
        }
        int[] z1 = new int[t[n-1]];
        int[] z2 = new int[t[n-1]];
        for(int i=0; i<t[n]; i++){
            if(a % 2 == 0){
                if(i % 2 == 0) z1[i/2] = z[i];
                if(i % 2 == 1) z2[i/2] = z[i];
            }
            if(a % 2 == 1){
                if(i % 2 == 0) z2[i/2] = z[i];
                if(i % 2 == 1) z1[i/2] = z[i];
            }
        }
        int start = 0;
        while(z1[start] != a) start++;
        int p = start;
        while(true){
            Console.Write(z1[p]+" ");
            if(z2[p] == b) break;
            Console.Write(z2[p]+" ");
            p++;
            if(p>=t[n-1]) p = 0;
        }
        int f = 0;
        while(true){
            if(p + 1 == start || (p + 1 == t[n-1] && start == 0)){
                f = 1;
                break;
            }
            p++;
            if(p>=t[n-1]) p = 0;
            Console.Write(z2[p]+" ");
            
            if(p + 1 == start || (p + 1 == t[n-1] && start == 0)){
                f = 2;
                break;
            }
            p++;
            if(p>=t[n-1]) p = 0;
            Console.Write(z1[p]+" ");
        }
        
        if(f == 1){
            p++;
            if(p>=t[n-1]) p = 0;
            while(true){
                p--;
                if(p<0) p = t[n-1] - 1;
                if(z2[p] == b) break;
                Console.Write(z2[p]+" ");
                p--;
                if(p<0) p = t[n-1] - 1;
                Console.Write(z1[p]+" ");
            }
        }
        if(f == 2){
            p++;
            if(p>=t[n-1]) p = 0;
            while(true){
                p--;
                if(p<0) p = t[n-1] - 1;
                Console.Write(z1[p]+" ");
                p--;
                if(p<0) p = t[n-1] - 1;
                if(z2[p] == b) break;
                Console.Write(z2[p]+" ");
            }
        }
        Console.WriteLine(b);
    }
    
    public static void DebugWL(object x){ System.Diagnostics.Debug.WriteLine(x); }
}