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:
import sys
u, v = map(int, input().split())
if (u > v):
    print(-1)
    sys.exit(0)
if (u == v and u == 0):
    print(0)
    sys.exit(0)
if (u == v):
    print(1)
    print(u)
    sys.exit(0)
if ((v - u) % 2 == 1):
    print(-1)
    sys.exit(0)
ans = [0] * 64
ans[0] = u
v -= u
for i in range(65, -1, -1):
    if (u & (1 << i)):
        j = 63
        while ((1 << i) * (j - 1) > v):
            j -= 2
        v -= (1 << i) * (j - 1)
        for k in range(1, j):
            ans[k] += (1 << i)
    else:
        j = 64
        while ((1 << i) * j > v):
            j -= 2
        v -= (1 << i) * j
        for k in range(j):
            ans[k] += (1 << i)
if (v != 0):
    print(-1)
    sys.exit(0)
i = 0
answ = []
while(ans[i] != 0):
    answ.append(ans[i])
    i += 1
print(len(answ))
print(*answ)