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 linput(a):
    return [int(i) for i in a.split()]

#q = int(input())
for ughblnk in range(1):
    u, v = linput(input())
    if u > v:
        print(-1)
    elif (u % 2) != (v % 2):
        print(-1)
    elif u == 0 and v == 0:
        print(0)
    elif u == v:
        print(1)
        print(u)
    else:
        t = (v - u) // 2
        bu = (bin(u)[2:])[::-1]
        bt = (bin(t)[2:])[::-1]
        i, q = 0, 0
        while i < len(bu) and i < len(bt) and q == 0:
            if bu[i] == bt[i] and bu[i] == "1":
                q = 1
            i += 1
        if q == 1:
            print(3)
            print(u, t, t)
        else:
            print(2)
            print((u + t), t)