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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author cunbidun
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CDifferBy1Bit solver = new CDifferBy1Bit();
        solver.solve(1, in, out);
        out.close();
    }

    static class CDifferBy1Bit {
        private ArrayList<Integer>[] adj = new ArrayList[131075];
        private boolean[] visited = new boolean[131075];
        private int[] p = new int[131075];
        int a;
        int b;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            a = in.nextInt();
            b = in.nextInt();
            for (int i = 0; i < 131073; i++) {
                p[i] = -1;
                adj[i] = new ArrayList<>();
            }
            for (int i = 0; i <= ((1 << n) - 1); i++) {
                for (int j = 0; j < n; j++) {
                    adj[i].add(i ^ (1 << j));
                }
            }
            visited[a] = visited[b] = true;
            dfs(a);
            int pos;
            for (int i : adj[b]) {
                if (p[i] != -1) {
                    pos = i;
                    ArrayList<Integer> num = new ArrayList<>();
                    while (pos != a) {
                        num.add(pos);
                        pos = p[pos];
                    }
                    if (num.size() != (((1 << n) - 1) - 1)) continue;
                    out.println("YES");
                    out.print(a + " ");
                    for (int j = num.size() - 1; j >= 0; j--) {
                        out.print(num.get(j) + " ");
                    }
                    out.println(b);
                    return;
                }
            }
            out.println("NO");
        }

        private void dfs(int u) {
            visited[u] = true;
            for (int v : adj[u]) {
                if (!visited[v]) {
                    p[v] = u;
                    dfs(v);
                }
            }
        }

    }

    static class InputReader extends InputStream {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private static boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}