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 = map(int, input().split())
a_str = bin(A)[2:]
b_str = bin(B)[2:]
a_bin = int(a_str)
b_bin = int(b_str)
a = [0] * (N+1)
b = [0] * (N+1)
c = [A] + [0]*(2**N-2) + [B]
# for i in range(len(a_str),2,-1):
# 	a.append(int(a_str[i-1]))
# for i in range(len(b_str),2,-1):
# 	b.append(int(b_str[i-1]))
cnta = 0
cntb = 0
while (a_bin):
	a[cnta] = a_bin%10
	a_bin = a_bin//10
	cnta += 1
while (b_bin):
	b[cntb] = b_bin%10
	b_bin = b_bin//10
	cntb += 1

# print(cnta,cntb)
d = A^B
h = 0
while(d):
	d &= d-1
	h += 1
# print(h)

if (2**N-h)%2 == 0 or h > 2**N-2:
	print('NO')
else:
	print('YES')
	j = 1
	C = A
	for i in range(max(cnta, cntb)):
		if a[i] != b[i]:
			if a[i] == 1:
				C -= 2**i
				c[j] = C
			else:
				C += 2**i
				c[j] = C
			j += 1
	for i in range(j,2**N-1,2):
		c[j],c[j+1] = c[j-2],c[j-1]
	for i in range(2**N):
		print(c[i], end=' ')