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 GETBIT(x, bit):
    return (x >> bit) & 1

def solve(u, v):
    if u > v:
        print(-1)
        return
    if v == 0:
        print(0)
        return
    v -= u
    if v == 0:
        print(1)
        print(u)
        return
    rs = 1
    lst = [0] * 3
    lst[0] += u
    if v % 2 == 1:
        print(-1)
        return
    for i in range(64):
        if GETBIT(v, i) == 1:
            if GETBIT(u, i-1) == 1:
                rs = max(rs, 3)
                lst[1] += (1 << (i-1))
                lst[2] += (1 << (i-1))
            else:
                rs = max(rs, 2)
                lst[1] += (1 << (i-1))
                lst[0] += (1 << (i-1))
    print(rs)
    print(*(lst[i] for i in range(rs)))


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