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:
u,v=list(map(int,input().split()))
def function(u,y):
    dict1={}
    a=bin(u)[2:]
    b=len(a)
    for i in range(b):
        if a[i]=="1":
            dict1[b-i]=1
    c=bin(y)[2:]
    d=len(c)
    for i in range(d):
        if c[i]=="1":
            if d-i in dict1.keys():
                return False
    return True
if u>v:
    print(-1)
elif u==v:
    if u==0:
        print(0)
    else:
        print(1)
        print(u)
else:
    x=v-u
    if x%2==1:
        print(-1)
    else:
        y=x//2
        if function(u,y):
            print(2)
            print(u|y,y)
        else:
            print(3)
            print(y,y,u)