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:
xor, sm = map(int, input().split())

diff = sm - xor

if diff < 0 or diff % 2:
    l = -1

else:
    if xor == sm == 0:
        l = 0

    elif xor == sm:
        l = 1
        ans = [sm]

    else:
        l = 2
        for i in range(60):
            if (xor >> i) & (diff >> (i + 1)):
                l = 3

        ans = [0] * l
        for i in range(60):
            j = 0
            if (xor >> i) & 1:
                ans[j] += 1 << i
                j += 1

            if (diff >> (i + 1)) & 1:
                ans[j] += 1 << i
                ans[j + 1] += 1 << i
                j += 2

print(l)
if l > 0:
    print(*ans)