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 u == v:
    if u > 0:
        ans = [u]
    else:
        ans = []
elif u > v:
    ans = None
else:
    diff = v - u
    if diff % 2:
        ans = None
    else:
        if (u + diff // 2) == (u ^ diff // 2):
            ans = [u + diff // 2, diff // 2]
        else:
            ans = [u, diff // 2, diff // 2]

if ans is None:
    print(-1)
else:
    print(len(ans))
    print(' '.join(map(str, ans)))
    if (sum(ans) != v):
        raise ValueError(ans)