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 python3
import sys
from math import *
from collections import defaultdict
from queue import deque                # Queues
from heapq import heappush, heappop    # Priority Queues

# parse
lines = [line.strip() for line in sys.stdin.readlines()]
u, v = list(map(int, lines[0].split()))

def f(u, v):
  if u > v:
    return None
  if u == 0 and v == 0:
    return []
  if u == v:
    return [u]
  y = v - u
  z = y // 2
  if y % 2 == 0:
    if (u + z) ^ z == u:
      return [u+ z, z]
    else:
      return [u, z, z]
  return None

xs = f(u, v)
if xs is None:
  print(-1)
else:
  print(len(xs))
  if xs:
    print(' '.join(map(str, xs)))