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:
"""
    Author : thekushalghosh
    Team   : CodeDiggers
"""
import sys,math
input = sys.stdin.readline
############ ---- USER DEFINED INPUT FUNCTIONS ---- ############
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(s[:len(s) - 1])
def invr():
    return(map(int,input().split()))
################################################################
############ ---- THE ACTUAL CODE STARTS BELOW ---- ############
t = 1
for tt in range(t):
    u, v = map(int, input().split())
    if u == 0 and v == 0:
        print(0)
        break
    elif u == 0 and v % 2 == 0:
        print(2)
        print(v // 2,v // 2)
        break
    elif u == 0 or v == 0:
        print(-1)
        break
    q = list(map(int,list(reversed(list("0" * (64 - int((math.log(u) // math.log(2)))) + bin(u).replace("0b", ""))))))
    w = list(map(int,list(reversed(list("0" * (64 - int((math.log(v) // math.log(2)))) + bin(v).replace("0b", ""))))))
    qw = 0
    for i in range(63,-1,-1):
        if w[i] % 2 == q[i]:
            continue
        if i == 0:
            qw = 1
            break
        if q[i] and w[i] == 0:
            for j in range(i + 1,64):
                if w[j] >= 2:
                    break
            else:
                qw = 1
            w[j] = w[j] - 2
            for k in range(i + 1,j):
                w[k] = w[k] + 2
            w[i] = w[i] + 4
        w[i] = w[i] -  1
        w[i - 1] = w[i - 1] + 2
    if qw == 1:
        print(-1)
    else:
        qwqw = [0] * max(w)
        for i in range(64):
            for j in range(w[i]):
                qwqw[j] = qwqw[j] + 2 ** i
        print(len(qwqw))
        print(*qwqw)