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
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__


u,v=list(map(int,input().split()))
if u>v:
    print(-1)
elif u==v:
    if u==0:
        print(0)
    else:
        print(1)
        print(u)
else:
    if u%2==0:
        if v%2==0:
            num=(v-u)//2

            num2=int(num&(u))
            if not num2:
                print(2)
                print(str(u+num)+" "+str(num))
            else:
                print(3)
                print(str(u)+" "+str(num)+" "+str(num))
        else:
            print(-1)
    else:
        if v%2==0:
            print(-1)
        else:
            num=(v-u)//2
            num2=int(num&(u))
            if not num2:
                print(2)
                print(str(u+num)+" "+str(num))
            else:
                print(3)
                print(str(u)+" "+str(num)+" "+str(num))