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:
u, v = [int(x) for x in input().split()]
if u == 0 and v == 0:
    print(0)
    exit(0)

if u == v:
    print(1)
    print(u)
    exit(0)
if u > v or (u-v)%2 == 1:
    print(-1)
    exit(0)

result = 0
tmp_u = u
tmp_and = (v-u) >> 1
x = tmp_and

i = 0
j = 0
# print(bin(tmp_u))
# print(bin(tmp_and))
while tmp_u > 0 or tmp_and > 0:
    a = tmp_and % 2
    b = tmp_u % 2
    if a == 1:
        if b == 1:
            print(3)
            print(u, x, x)
            exit(0)
        if b == 0:
            result = result + (1<<i)
    if b == 1:
        j = i
    tmp_u = tmp_u>>1
    tmp_and = tmp_and>>1
    i += 1

print(2)
print(result, v-result)