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:
u, v = map(int, input().split())
if v < u or (v - u) % 2 != 0:
    print(-1)
else:
    if u == v:
        if u == 0:
            print(0)
        else:
            print("1\n" + str(u))
    else:
        w = (v - u) // 2
        if (w | u) == (w + u):
            print("2\n" + str(w|u) + ' ' + str(w))
        else:
            print("3\n" + str(u) + ' ' + str(w) + ' ' + str(w))