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:
u, v = map(int, input().split())
A = (v - u) // 2
if A < 0 or (v - u) % 2 != 0:
    print(-1)
elif u == 0 and v == 0:
    print(0)
else:
    a = 0
    b = 0
    c = 0
    for i in range(61):
        ui = (u & (1 << i))
        Ai = (A & (1 << i))
        # print(ui)
        # print(Ai)
        if ui == 0 and Ai > 0:
            a = ((1 << i) | a)
            b = ((1 << i) | b)

        elif ui > 0 and Ai == 0:
            a = ((1 << i) | a)

        elif ui > 0 and Ai > 0:
            c = ((1 << i) | c)
            a = ((1 << i) | a)
            b = ((1 << i) | b)

    if b == 0:
        print(1)
        print(a)
    elif c == 0:
        print(2)
        print(a, b)
    else:
        print(3)
        print(a, b, c)