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:
import sys

readline = sys.stdin.readline

ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))

def solve():
    u, v = nm()
    if u == v:
        if u == 0:
            print(0)
        else:
            print(1)
            print(u)
        return
    elif u > v:
        print(-1)
        return
    w = v - u
    if w & 1:
        print(-1)
    else:
        l = [u, w//2, w//2]
        if not l[0] & l[-1]:
            l[0] ^= l.pop()
        print(len(l))
        print(*l)

    return

solve()

# T = ni()
# for _ in range(T):
#     solve()