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:
a,b=map(int,input().split())

def f(a,b):
    if b-a<0 or (b-a)%2==1:
        print(-1)
    elif b==0:
        print(0)
    elif a==b:
        print(1)
        print(b)
    else:
        x = (b-a)//2
        if a^x==a+x:
            sol=[a+x, x]
        else:
            sol=[a, x, x]
        
        print(len(sol))
        print(' '.join([str(i) for i in sol]))

f(a,b)