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:
from math import *
from operator import *
import sys, random

def nextInt():
    return int(input())
def nextStrs():
    return input().split()
def nextInts():
    return list(map(int,nextStrs()))

def main():
    t = 1

    for _ in range(t):
        u,v = nextInts()

        if u > v:
            print(-1)
        elif u == v:
            print('0' if u == 0 else f'1\n{u}')
        else:
            if u%2 != v%2:
                print(-1)
            else:
                div = (v-u)//2
                if (xor(u,div)) == div+u:
                    print(f'2\n{u+div} {div}')
                else:
                    print(f'3\n{u} {div} {div}')
                          
if __name__ == '__main__':
    exit(main())