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():
    import sys
    input = sys.stdin.buffer.readline

    u, v = map(int, input().split())
    if u > v:
        print(-1)
        exit()
    if u & 1 != v & 1:
        print(-1)
        exit()
    if u == v == 0:
        print(0)
        exit()
    a = 0
    b = 0
    w = (v - u) >> 1
    for i in range(100):
        if w >> i & 1:
            if u >> i & 1:
                a ^= (1<<i)
                b ^= (1<<i)
            else:
                a ^= (1<<i)
                u ^= (1<<i)
    ans = [u]
    if a:
        ans.append(a)
    if b:
        ans.append(b)
    print(len(ans))
    print(*ans)


if __name__ == '__main__':
    main()