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:
#JMD
#Nagendra Jha-4096

 
import sys
import math

#import fractions
#import numpy
 
###File Operations###
fileoperation=0
if(fileoperation):
    orig_stdout = sys.stdout
    orig_stdin = sys.stdin
    inputfile = open('W:/Competitive Programming/input.txt', 'r')
    outputfile = open('W:/Competitive Programming/output.txt', 'w')
    sys.stdin = inputfile
    sys.stdout = outputfile

###Defines...###
mod=1000000007
 
###FUF's...###
def nospace(l):
    ans=''.join(str(i) for i in l)
    return ans
 
 
 
##### Main ####

def is2(u,v):
    annd=(v-u)//2
    a=0
    b=0

    for i in range(64):
        val= (1<<i)

        if(val & u == 0):
            if(val & annd):
                a+=val
                b+=val
        else:
            a+=val
    if(a^b==u and a+b==v):
        print(2)
        print(a,b)
        return True
    return False

t=1
for tt in range(t):
    #n=int(input())
    u,v= map(int, sys.stdin.readline().split(' '))

    if(u==0 and v==0):
        print(0)
        continue

    if(u==v):
        print(1)
        print(u)
        continue

    if( ((v-u)%2!=0) or (u>v)):
        print(-1)
        continue

    if(is2(u,v)):
        continue

    d=(v-u)
    dd=d//2

    print(3)
    print(u,dd,dd)
    
    
#####File Operations#####
if(fileoperation):
    sys.stdout = orig_stdout
    sys.stdin = orig_stdin
    inputfile.close()
    outputfile.close()