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 C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

int n, a, b, m = 1;
bool f[131072];
vector<int> v, w;

int main(){
//	cin.tie(0);
//	ios::sync_with_stdio(false);
	cin >> n >> a >> b;
	for(int i=0; i<n; ++i) m <<= 1;
	int cnt = 0;
	for(int i=0; i<n; ++i)
		if(((a >> i) & 1) != ((b >> i) & 1))
			++cnt;
	if(cnt % 2 == 0){
		cout << "NO\n";
		return 0;
	}
	int t = a, u = b;
	v.push_back(t);
	w.push_back(u);
	f[t] = true;
	f[u] = true;
	while(1){
		vector<int> x, y;
		for(int i=0; i<n; ++i){
			if(!f[t^(1<<i)]){
				x.push_back(t^(1<<i));
			}
			if(!f[u^(1<<i)]){
				y.push_back(u^(1<<i));
			}
		}
		sort(x.begin(), x.end());
		sort(y.begin(), y.end());
		t = x[0];
		f[t] = true;
		v.push_back(t);
		u = y[0];
		f[u] = true;
		w.push_back(u);
		if(v.size() + w.size() == m) break;
	}
	cout << "YES\n";
	for(int i=0; i<v.size(); ++i)
		cout << v[i] << " ";
	for(int i=w.size()-1; i>=0; --i)
		cout << w[i] << (i == 0 ? "\n" : " ");
}