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:
x, s = map(int, input().split())
t = (s - x) // 2
a = 0
b = 0
f = 0
if (x > int(s)) or (int(x) % 2) != (int(s) % 2):
    print(-1)
elif int(x) == 0 and int(s) == 0:
    print(0)
elif x == s:
    print(1)
    print(x)
else:
    for i in range(64):
        y = (x & (1 << i))
        z = (t & (1 << i))
        if y == 0 and z == 0:
            continue
        elif y == 0 and z > 0:
            a = ((1 << i) | a)
            b = ((1 << i) | b)
        elif y > 0 and z == 0:
            a = ((1 << i) | a)
        else:
            f = 1
            break

    if f == 0:
        print(2)
        print(a, b)
    else:
        print(3)
        print(int(x), t, t)