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:
# cook your dish here

def compute(x,s): 
    rem = (s-x)//2
    a,b = 0,0
    
    for i in range(64): 
        j=(x&(1<<i))
        k=(rem&(1<<i))
        if (j==0 and k==0):  
            pass
        elif (j==0 and k>0): 
            a=((1<<i)|a)
            b=((1<<i)|b)
        elif (j>0 and k==0): 
            a=((1<<i)|a)
        else:
            print(3)
            print(x,rem,rem)
            return 
  
    print(2)
    print(a,b)

#for _ in range(int(input())):
x,s=map(int,input().split())
if (x==0 and s==0):
    print(0)
elif (x==s):
    print(1)
    print(x)
elif (x>s or (x-s)%2==1):
    print(-1)
else:
    compute(x,s)