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:
a,b = (int(i) for i in input().split(' '))
d = {}
def lowbit(u):
    return u&(-u)
if a > b or (b-a) & 1:
    print(-1)
elif b == a and a == 0:
    print(0)
else:
    if b == a:
        print(1)
        print(a)
    else:
        a1 = a
        a2 = (b-a)>>1
        if a2&a1:
            print(3)
            print(a1,a2,a2)
        else:
            print(2)
            print(a1+a2,a2)