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 f(a):
    b = 0

    while a > 0:
        b += 1
        a //= 2

    return 2 ** (b - 1)

u, v = map(int, input().split())

if u > v:
    print(-1)
elif u == v == 0:
    print(0)
elif u == v:
    print(1)
    print(v)
else:
    k = 0
    
    while True:
        if u == 0:
            break

        c = f(u)
        u -= c
        v -= c
        k += c

    if v % 2 == 1:
        print(-1)
    else:
        if k & (v // 2) == 0:
            k += v // 2
            print(2)
            print(k, v // 2)
        else:
            print(3)
            print(k, v // 2, v // 2)