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 ll = long long int;
using namespace std;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  ll u, v;
  cin >> u >> v;
  if ((v < u) || ((u % 2) != (v % 2))) {
    cout << -1;
    return 0;
  }
  ll d = (v - u) / 2;
  if (d == 0) {
    if (v == 0)
      cout << 0;
    else {
      cout << 1 << "\n" << v;
    }
    return 0;
  }
  if (((u + d) ^ d) == u) {
    cout << 2 << "\n";
    cout << u + d << " " << d;
  } else {
    cout << 3 << "\n";
    cout << u << " " << d << " " << d;
  }
  cout << "\n";
  return 0;
}