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
input=sys.stdin.readline
from math import *

    
k,m=map(int,input().split())
if k>m:
    print(-1)
    exit(0)
r=list(bin(k))[2:]
n=len(r)
for i in range(n):
    if r[i]=='1':
        m-=2**(n-i-1)
if m&1:
    print(-1)
    exit(0)
#print(m)    
l=list(bin(m//2))[2:]
f=[0 for i in range(60)]
for i in range(len(l)):
    if l[i]=='1':
        f[len(l)-i-1]+=2
 
for i in range(len(r)):
    if r[i]=='1':
        f[len(r)-i-1]+=1
d=[]
#print(f)
while f.count(0)!=len(f):
    g=0
    for i in range(60):
        if f[i]>0:
            f[i]-=1
            g+=2**i
    d.append(g)
print(len(d))
print(*d)