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 bisect, collections



def solution():
    u, v = [int(x) for x in input().strip().split(" ")]
    if u == v:
        if u == 0:
            print(0)
        else:
            print(1)
            print(u)
    elif u > v or (v-u) % 2 == 1:
        print(-1)
    else:
        k = (v-u)//2
        if k & u == 0:
            print(2)
            print(k|u, k)
        else:
            print(3)
            print(u, k, k)
    

    


def main():    
    # T = int(input().strip())
    for _ in range(1):
        solution()
    

main()