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:
from sys import exit

v, u = map(int, input().split())
arr = []
for i in range(64):
    if ((v>>i)&1):
        arr.append(1<<i)

x = u - v
if x < 0 or x % 2 != 0:
    print(-1)
    exit(0)
for i in range(64):
    if ((x>>i)&1):
        arr.append(1<<(i - 1))
        arr.append(1<<(i - 1))

for i in range(len(arr)):
    for b in range(0, 64):
        if ((arr[i]>>b)&1) == 0:
            continue
        for j in range(i + 1, len(arr)):
            if ((arr[j]>>b)&1) == 1:
                continue
            arr[j] |= (1<<b)
            arr[i] &= ~(1<<b)
            break

brr = []
for el in arr:
    if el == 0:
        continue
    brr.append(el)

print(len(brr))
print(*brr)