Problem: Mahmoud and Ehab are on the third stage of their adventures now. As you know, Dr. Evil likes sets. This time he won't show them any set from his large collection, but will ask them to create a new set to replenish his beautiful collection of sets.

Dr. Evil has his favorite evil integer x. He asks Mahmoud and Ehab to find a set of n distinct non-negative integers such the bitwise-xor sum of the integers in it is exactly x. Dr. Evil doesn't like big numbers, so any number in the set shouldn't be greater than 106.

Input

The only line contains two integers n and x (1 ≤ n ≤ 105, 0 ≤ x ≤ 105) — the number of elements in the set and the desired bitwise-xor, respectively.

Output

If there is no such set, print "NO" (without quotes).

Otherwise, on the first line print "YES" (without quotes) and on the second line print n distinct integers, denoting the elements in the set is any order. If there are multiple solutions you can print any of them.

Examples

Input

5 5


Output

YES
1 2 4 5 7

Input

3 6


Output

YES
1 2 5

Note

You can read more about the bitwise-xor operation here: <https://en.wikipedia.org/wiki/Bitwise_operation#XOR>

For the first sample <image>.

For the second sample <image>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,no-stack-protector")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,tune=native")
using namespace std;
const int INF = 1000 * 1000 * 1000 + 322;
const long long LLINF =
    2LL * 1000LL * 1000LL * 1000LL * 1000LL * 1000LL * 1000LL + 57;
const int MOD = 1000 * 1000 * 1000LL + 7;
const long long FFT_MOD = 998244353;
const int P1M = 1336337;
const int P1K = 1009;
const double EPS = 1e-14;
const double PI = acos(-1.);
template <typename T, typename U>
inline ostream &operator<<(ostream &_out, const pair<T, U> &_p) {
  _out << _p.x << " " << _p.y;
  return _out;
}
template <typename T, typename U>
inline istream &operator>>(istream &_in, pair<T, U> &_p) {
  _in >> _p.x >> _p.y;
  return _in;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const vector<T> &_v) {
  if (_v.empty()) return _out;
  _out << _v.front();
  for (auto _it = ++_v.begin(); _it != _v.end(); ++_it) _out << ' ' << *_it;
  return _out;
}
template <typename T>
inline istream &operator>>(istream &_in, vector<T> &_v) {
  for (auto &_i : _v) _in >> _i;
  return _in;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const set<T> &_s) {
  if (_s.empty()) return _out;
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) _out << ' ' << *_it;
  return _out;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const multiset<T> &_s) {
  if (_s.empty()) return _out;
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) _out << ' ' << *_it;
  return _out;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const unordered_set<T> &_s) {
  if (_s.empty()) return _out;
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) _out << ' ' << *_it;
  return _out;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const unordered_multiset<T> &_s) {
  if (_s.empty()) return _out;
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) _out << ' ' << *_it;
  return _out;
}
template <typename T, typename U>
inline ostream &operator<<(ostream &_out, const map<T, U> &_m) {
  if (_m.empty()) return _out;
  _out << '(' << _m.begin()->x << ": " << _m.begin()->y << ')';
  for (auto _it = ++_m.begin(); _it != _m.end(); ++_it)
    _out << ", (" << _it->x << ": " << _it->y << ')';
  return _out;
}
template <typename T, typename U>
inline ostream &operator<<(ostream &_out, const unordered_map<T, U> &_m) {
  if (_m.empty()) return _out;
  _out << '(' << _m.begin()->x << ": " << _m.begin()->y << ')';
  for (auto _it = ++_m.begin(); _it != _m.end(); ++_it)
    _out << ", (" << _it->x << ": " << _it->y << ')';
  return _out;
}
const char *infile = "";
const char *outfile = "";
inline long long gcd(long long a, long long b) {
  while (b) {
    a %= b;
    swap(a, b);
  }
  return a;
}
inline long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
inline long long pwm(long long xx, long long pow, long long MD = MOD) {
  long long mlt = 1;
  while (pow) {
    if (pow & 1) {
      mlt *= xx;
      xx *= xx;
      pow >>= 1;
      xx %= MD;
      mlt %= MD;
    } else {
      pow >>= 1;
      xx *= xx;
      xx %= MD;
    }
  }
  return mlt;
}
inline long long inv(long long r, long long _mod = MOD) {
  return pwm(r % _mod, _mod - 2, _mod);
}
inline void solve() {
  int n;
  cin >> n;
  int x;
  cin >> x;
  int pw2 = (1 << 18);
  assert(pw2 > 100 * 1000 && pw2 < 900 * 1000);
  if (n & 1) {
    cout << "YES\n";
    int xr = 0;
    for (int i = 0; i < n - 1; ++i) {
      cout << i + pw2 << " ";
      xr ^= (pw2 + i);
    }
    cout << (xr ^ x) << endl;
  } else {
    if (n == 2 && x == 0) {
      cout << "NO\n";
      return;
    }
    cout << "YES\n";
    int xr = 0, i;
    for (i = 0; i < n - 3; ++i) {
      cout << i + pw2 << " ";
      xr ^= (pw2 + i);
    }
    if (n != 2) {
      if ((xr ^ (pw2 + i)) == x) {
        cout << pw2 + i + 1 << " ";
        xr ^= (pw2 + i + 1);
      } else {
        cout << pw2 + i << " ";
        xr ^= (pw2 + i);
      }
    }
    cout << 0 << " " << (xr ^ x) << endl;
  }
}
int main() {
  if (*infile != '\0') (void)freopen(infile, "r", stdin);
  if (*outfile != '\0') (void)freopen(outfile, "w", stdout);
  cout.tie(nullptr);
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << setprecision(20);
  cout << fixed;
  solve();
  return 0;
}