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 == 0 and v == 0:
    print(0)
elif u == v:
    print(1)
    print(u)
elif (v - u < 2 or (v - u) % 2 == 1):
    print(-1)
else:
    ex = (v - u) // 2
    if (ex & u == 0):
        print(2)
        print(ex | u, ex)
    else:
        print(3)
        print(u, ex, ex)