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 Python (3.4.3) (judge verdict: Accepted)

N, A, B = map(int, input().split())


def f(n, a, b):
    if n == 1:
        return [a, b]

    mask = 1 << (n-1)
    if a & mask == b & mask:
        v1 = f(n-1, a, b)
        v2 = f(n-1, a ^ mask, v1[1] ^ mask)
        ret = v1[:1]
        ret.extend(v2)
        ret.extend(v1[1:])
        return ret
    else:
        v1 = f(n-1, a, a ^ 1)
        v2 = f(n-1, a ^ 1 ^ mask, b)
        v1.extend(v2)
        return v1


if bin(A ^ B).count('1') % 2 == 0:
    print("NO")
else:
    print("YES")
    res = f(N, A, B)
    for p in res:
        print(p)