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;
void solve(long long u, long long v) {
  if (u > v)
    cout << "-1" << endl;
  else if ((v - u) % 2 == 1)
    cout << "-1" << endl;
  else if (v == 0)
    cout << "0" << endl;
  else if (u == v)
    cout << "1" << endl << u << endl;
  else {
    long long t = (v - u) / 2;
    if (!(u & t))
      cout << "2" << endl << u + t << " " << t << endl;
    else
      cout << "3" << endl << u << " " << t << " " << t << endl;
  }
}
int main() {
  long long u, v;
  cin >> u >> v;
  solve(u, v);
  return 0;
}