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:
#!/usr/bin/env python
#-*- coding:utf-8 -*-

# Code by H~$~C

from sys import stdin
input = stdin.readline
import math

u, v = map(int, input().split())
if (u == v):
  if (u == 0):
    print(0)
    exit(0)
  print(1)
  print(u)
  exit(0)
if (u > v):
  print('-1')
  exit(0)
if ((v - u) % 2):
  print('-1')
  exit(0)

p = (v - u) // 2
if ((u & p) == 0):
  print(2)
  print(p, u + p, sep = ' ')
  exit(0)

print(3)
print(u, p, p, sep = ' ')