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


def main():
    u, v = map(int, input().split())
    v -= u
    if u == v == 0:
        print(0)
        return
    if v < 0:
        print('-1')
        return
    if v == 0:
        print(1)
        print(u)
        return
    if v % 2 != 0:
        print("-1")
        return
    else:
        if ((v // 2) & u) != 0:
            print(3)
            print(u, v // 2, v // 2)
            return
        else:
            print(2)
            print(u + (v // 2), v // 2)
            return



if __name__ == "__main__":
    t = 1
    for i in range(t):
        main()