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 sys
import math

def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def read():  return int(input())
def reads(): return map(int, sys.stdin.readline().strip().split())
def input(): return sys.stdin.readline().strip() #strip() avoid reading '\n'



#-- main --#

u, v = reads()

if (u > v) or ((u & 1) != (v & 1)):
    print(-1)
else:
    if u == 0 and v == 0:
        print(0)
    elif u == v:
        print(1)
        print(u)

    else:
        w = v - u >> 1
        o = w & u
        if o:
            print(3)
            print(w, w, u)
        else:
            print(2)
            print(w + u, w)