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 sol():
    u, v = map(int, input().split())
    if u > v or (u-v) % 2 != 0:
        return -1
    if u == v:
        if u == 0:
            return 0
        else:
            return '1\n%d' % u
    x = (v-u) // 2

    a, b = 0, 0
    i = 1
    u_ = u 
    x_ = x
    while u_ or x_:
        m, n = u_%2, x_%2
        if n == 1:
            if m == 1:
                return '3\n{} {} {}'.format(u, x, x)
            else:
                a += i 
                b += i 
        else:                
            if m == 1:
                a += i 
        u_ //= 2
        x_ //= 2
        i *= 2
    return '2\n%d %d' % (a, b)
print(sol())