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 Rust (1.15.1) (judge verdict: Wrong Answer)

#![allow(unused_imports)]
use std::io::{ self, Write };
use std::str::FromStr;
use std::cmp::{ min, max };
use std::collections::{ BinaryHeap, VecDeque };

#[allow(unused_macros)]
macro_rules! trace {
    ($var:expr) => {
        let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($var), $var);
    };
    ($($args:expr),*) => {
        let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($($args),*), ($($args),*));
    };
}

#[allow(unused_macros)]
macro_rules! put {
    ($var:expr) => {
        let _ = writeln!(&mut std::io::stdout(), "{}", $var);
    };
    ($var:expr, $($args:expr),*) => {
        let _ = write!(&mut std::io::stdout(), "{} ", $var);
        put!($($args),*);
    };
}

fn gray(v: usize) -> usize {
    v ^ (v >> 1)
}

fn main() {

    for i in 0..32 { println!("{:05b}", gray(i));}
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let mut a: usize = sc.cin();
    let mut b: usize = sc.cin();

    if (a ^ b).count_ones() % 2 == 0 {
        put!("NO");
        return;
    }
    put!("YES");

    // let mut next_g = vec![0; 1 << n];
    // {
    //     let mut last_g = 0;
    //     for i in 1..(1<<n) {
    //         let g = gray(i);
    //         next_g[last_g] = g;
    //         last_g = g;
    //     }
    // }
    // trace!(next_g);
    //
    // let c = a ^ b;
    // // let ones = c.count_ones();
    // // let zeros = n - c.count_ones();
    //
    //
    // let mut reverse = false;
    //
    // let mut c = 0;
    // {
    //     for x in 0..(1<<n) {
    //         if next_g[a^x] == b^x {
    //             trace!((a,b,x), b^x);
    //             c = x;
    //             break;
    //         }
    //         if next_g[b^x] == a^x {
    //             reverse = true;
    //             trace!(reverse);
    //             c = a;
    //             a = b;
    //             b = c;
    //             c = x;
    //             trace!((a,b,x), b^x);
    //         }
    //     }
    // }
    // trace!(c, a ^ c, b ^ c);

}

#[allow(dead_code)]
struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn reserve(&mut self) {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        self.reserve();
        match self.buffer.pop_front().unwrap().parse::<T>() {
            Ok(a) => a,
            Err(_) => panic!("parse err")
        }
    }
}