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: Wrong Answer)

N, A, B = [int(x) for x in input().split(' ') ]

possible = False
for i in range(N):
  if A ^ (1 << i) == B:
    possible = True
if not possible:
  print('NO')
else:
  print('YES')
  list = [A]
  visited = [False] * (2**N)
  visited[A] = True
  visited[B] = True
  current = A
  for i in range(2**N - 2):
    for j in range(N):
      x = current ^ (1 << j)
      if not visited[x]:
        visited[x] = True
        list.append(x)
        current = x
        break
  list.append(B)
  for x in list:
    print(x, end=" ")