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:
def main():
    x, y = list(map(int, input().split()))
    if x > y:
        print(-1)
    elif x == 0 and y == 0:
        print(0)
    elif x == y:
        print(1)
        print(x)
    elif (y // 2 - x // 2) ^ (y // 2 + (x + 1) // 2) == x \
            and (y // 2 - x // 2) + (y // 2 + (x + 1) // 2) == y:
        print(2)
        print(y // 2 - x // 2, y // 2 + (x + 1) // 2)
    elif (y - x) % 2 == 0:
        print(3)
        print(x, (y - x) // 2, (y - x) // 2)
    else:
        print(-1)


if __name__ == '__main__':
    main()