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 PYTHON3):

Solution:

import math

a ,b =map(int,input().split())

if a==b:
    if a==0:
        print(0)
    else:
        print(1)
        print(a)

else:
    if a>b:
        print(-1)
    else:
        if a==0:
            if b%2==0:
                print(2)
                print(b//2,b//2)
            else:
                print(-1)

        else:


            if (b-a)%2==0:
                if (((int((b-a)//2)) ^int(((b+a)//2))) == a):
                    print(2)
                    print((b-a)//2 ,(b+a)//2)
                else:
                    print(3)
                    print(a,(b-a)//2,(b-a)//2)
            else:
                print(-1)