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:
def func(S, X):
    A = (S - X)//2
    a = 0
    b = 0
    for i in range(64):
        Xi = (X & (1 << i))
        Ai = (A & (1 << i)) 
        if (Xi == 0 and Ai == 0):
            pass
        elif (Xi == 0 and Ai > 0):
            a = ((1 << i) | a)
            b = ((1 << i) | b)
        elif (Xi > 0 and Ai == 0):
            a = ((1 << i) | a)
        else:
            print(3)
            print(x,A,A)
            return
    print(2)
    print(a,b)

x,s = list(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:
    func(s,x)