Problem: Given 2 integers u and v, find the shortest array such that [bitwise-xor](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of its elements is u, and the sum of its elements is v.

Input

The only line contains 2 integers u and v (0 ≤ u,v ≤ 10^{18}).

Output

If there's no array that satisfies the condition, print "-1". Otherwise:

The first line should contain one integer, n, representing the length of the desired array. The next line should contain n positive integers, the array itself. If there are multiple possible answers, print any.

Examples

Input


2 4


Output


2
3 1

Input


1 3


Output


3
1 1 1

Input


8 5


Output


-1

Input


0 0


Output


0

Note

In the first sample, 3⊕ 1 = 2 and 3 + 1 = 4. There is no valid array of smaller length.

Notice that in the fourth sample the array is empty.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class T>
ostream& operator<<(ostream& os, vector<T> V) {
  os << "[ ";
  for (auto v : V) os << v << " ";
  return os << "]";
}
template <class T>
ostream& operator<<(ostream& os, set<T> S) {
  os << "{ ";
  for (auto s : S) os << s << " ";
  return os << "}";
}
template <class L, class R>
ostream& operator<<(ostream& os, pair<L, R> P) {
  return os << "(" << P.first << "," << P.second << ")";
}
template <class L, class R>
ostream& operator<<(ostream& os, map<L, R> M) {
  os << "{ ";
  for (auto m : M) os << "(" << m.F << ":" << m.S << ")";
  return os << "}";
}
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cout << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cout.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << fixed << setprecision(25);
  long long u, v;
  cin >> u >> v;
  if ((abs(u - v)) % 2 != 0 || u > v) {
    cout << -1 << "\n";
    return 0;
  }
  if (u == v) {
    if (u == 0) {
      cout << 0 << "\n";
      return 0;
    }
    cout << 1 << "\n";
    cout << u << "\n";
    return 0;
  }
  long long band = v - u;
  band /= 2;
  long long ans = 0;
  long long a = 0, b = 0;
  for (int i = 0; i < 63; ++i) {
    bool aa = (band & (1ll << i));
    bool bb = (u & (1ll << i));
    if (aa && bb) {
      cout << 3 << "\n";
      cout << u << ' ' << band << ' ' << band << "\n";
      return 0;
    }
    if (aa && !bb) {
      a += (1ll << i);
      b += (1ll << i);
    }
    if (bb && !aa) {
      a += (1ll << i);
    }
  }
  cout << 2 << "\n";
  cout << a << ' ' << b << "\n";
  return 0;
}