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:
from sys import stdin    
def mp():return map(int,stdin.readline().split())
def ml():return list(map(int,stdin.readline().split()))

xor,sm=mp()
if xor> sm:print(-1)
else:
    if (sm-xor)%2==1:print(-1)
    else:
        n1=xor;n2=(sm-xor)//2
        if n1==0 and n2==0: print(0)
        elif n2==0:
            print(1);print(n1)
        elif (n2+n1)^n2==xor :
            print(2);print(n2+n1,n2)
        elif(n2+n2)^n1==xor:
            print(2);print(n2+n2,n1)
        else: 
            print(3)
            print(n1,n2,n2)