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;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  long long int S, X;
  cin >> X >> S;
  if (S + X == 0)
    cout << 0 << endl;
  else if (S == X)
    cout << 1 << endl << S;
  else if (S < X || S % 2 != X % 2)
    cout << -1 << endl;
  else if (X & ((S - X) / 2))
    cout << 3 << endl << X << " " << (S - X) / 2 << " " << (S - X) / 2;
  else
    cout << 2 << endl << (X + (S - X) / 2) << " " << (S - X) / 2;
}