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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class D {

    private void work() {
        Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in), 1 << 16));
        long u = sc.nextLong();
        long v = sc.nextLong();
        sc.close();

        if (u > v) {
            System.out.println(-1);
            return;
        }

        if (u == v) {
            if (u == 0) System.out.println(0);
            else System.out.printf("1\n%d\n", u);
            return;
        }

        long d = v - u;
        if ((d & 1) != 0) {
            System.out.println(-1);
            return;
        }

        d >>= 1;
        if (((u + d) ^ d) == u) {
            System.out.printf("2\n%d %d\n", u + d, d);
        } else {
            System.out.printf("3\n%d %d %d\n", u, d, d);
        }
    }

    public static void main(String[] args) {
        new D().work();
    }
}