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 PYTHON):

Solution:
x, s = map(int, raw_input().split())

dif = s-x
if dif < 0: print -1
elif s == 0: print 0
elif x == s: 
    print 1
    print x
elif dif%2 == 0:
    if (dif/2)^x == (dif/2)|x: 
        print 2
        print dif/2, (dif/2)|x
    else:
        print 3
        print dif/2, dif/2, x
else: print -1