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

count = [0] * 100
index = 0

works = True
while u >= 0 and v >=0 and (v > 0 or u > 0):
    u2 = u & 1
    v2 = v & 1
    if u2 != v2:
        u -= 1
        if index:
            count[index - 1] += 2
        else:
            works = False
            break
    elif u2:
        u -= 1
        v -= 1
        count[index] += 1
    else:
        u >>= 1
        v >>= 1
        index += 1

if works and u >= 0 and v >= 0:
    out = []
    for i in range(100):
        while len(out) < count[i]:
            out.append(0)
        for j in range(count[i]):
            out[j] ^= 1 << i
    print(len(out))
    print(' '.join(map(str,out)))
else:
    print(-1)