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 collections import defaultdict
a, b = map(int, input().strip().split())

bb = [0] * 64

ps = 0

cnt = [0] * 64

ma = 0

for i in range(64):
    b0 = (a >> i) & 1
    b1 = (b >> i) & 1

    if b0:
        cnt[i] += 1
        ps += 1
    if (ps&1) != b1:
        if i == 0:
            print(-1)
            exit(0)
        cnt[i-1] += 2
        ps += 1
    ps = ps // 2

if ps:
  print(-1)
  exit(0)

for i in range(64):
    ma = max(ma, cnt[i])

ans = [0,0,0]

for i in range(64):
    for j in range(cnt[i]):
        ans[j] += 1 << i

print(ma)
answ = ""
for x in range(ma):
    answ +="{} ".format(ans[x])
print(answ)