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_function():
    u, v = list(map(int, input().split(' ')))
    if u > v or (v - u) % 2 == 1:
        print('-1')
    elif (v - u) % 2 == 0:
        sup_num = (v - u) // 2
        A = [sup_num, u+sup_num]
        if A[0] ^ A[1] == u:
            if A[0] != 0:
                print(2)
            else:
                print(1 if u != 0 else 0)
                A = [u] if u != 0 else []
            print(*A)
        else:
            print(3)
            print(sup_num, sup_num, u)
    else:
        print('ghost or phantom')


if __name__ == '__main__':
    main_function()