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 functools import  reduce
def to_bits(x):
    bits = [0] * 64
    for i in range(64):
        bits[i] = x & 1
        x >>= 1
    return bits
u, v = map(int, input().split())
bu = to_bits(u)
bv = to_bits(v)
cnt = [0] * 64
if bu[0] != bv[0] or u > v:
    print(-1)
    exit()
act = 0
cnt[0] = bu[0]
for i in range(1, 64):
    act //= 2
    cnt[i] = bu[i]
    bv[i] ^= act
    if bu[i] != bv[i]:
        cnt[i - 1] += 2
        act += 1
    act += cnt[i]
ans = max(cnt)
arr = [0] * ans
msk = 1
for i in range(64):
    for j in range(cnt[i]):
        arr[j] += msk
    msk <<= 1
print(ans)
print(*arr)