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:
u,v = map(int, input().split())

def xorcise(u, v):
    if u > v or (v&1 != u&1):
        print(-1)
        return

    m = v.bit_length()
    r_bits = list(map(int, reversed(format(v-u, "b").zfill(m))))

    x = u
    y = 0
    z = 0

    for b in range(m-1):
        d = 1 << b

        if r_bits[b+1]:
            if x&d:
                y += d
                z += d
            else:
                x += d
                y += d

    out = []
    if x: out.append(x)
    if y: out.append(y)
    if z: out.append(z)
    print(len(out))
    if out: print(*out)

xorcise(u, v)