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:
# https://codeforces.com/contest/1325/problem/D

# import sys
# # input = sys.stdin.buffer.readline
# def input(): return sys.stdin.readline().rstrip()
# sys.setrecursionlimit(10 ** 7)


def main():
    u, v = map(int, input().split())
    dif = v-u
    if dif < 0 or dif%2:
        print(-1)
        return
    elif dif == 0 and u == 0:
        print(0)
        return
    elif dif == 0:
        ans = [u]
    else:
        half = dif >> 1
        rest = v - 2 * half
        if rest & half:
            ans = [half, half, rest]
        else:
            ans = [half, half+rest]
    print(len(ans))
    print(*ans)

    # from functools import reduce
    # print(reduce(lambda x, y: x ^ y, ans), sum(ans))
    return

main()