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 io
import os

from collections import Counter, defaultdict, deque


def solve(U, V):
    if U == V == 0:
        return 0
    binU = [int(d) for d in bin(U)[2:]][::-1]
    binV = [int(d) for d in bin(V)[2:]][::-1]

    N = max(len(binU), len(binV))
    while len(binU) < N:
        binU.append(0)
    while len(binV) < N:
        binV.append(0)
    assert len(binU) == len(binV) == N

    ones = defaultdict(int)
    if binU[0] != binV[0]:
        return -1
    if binU[0] == 1:
        ones[0] += 1

    carries = ones[0] // 2
    for i in range(1, N):

        if ones[i] % 2 != binU[i]:
            ones[i] += 1
        if ((ones[i] + carries) % 2) != binV[i]:
            # Add 2 to i-1 or 1 to ones[i]
            ones[i - 1] += 2
            carries += 1
        if False:
            assert ones[i] % 2 == binU[i]
            assert (ones[i] + carries) % 2 == binV[i]

        carries = (ones[i] + carries) // 2
    if carries != 0:
        return -1

    outN = max(ones.values())
    arr = []
    for i in range(outN):
        temp = 0
        for j in range(N):
            if i < ones[j]:
                temp += 1 << j
        arr.append(temp)

    if False:
        check1 = 0
        check2 = 0
        for x in arr:
            check1 ^= x
            check2 += x
        assert check1 == U
        assert check2 == V

    return str(len(arr)) + "\n" + " ".join(map(str, arr))


if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    U, V = [int(x) for x in input().split()]
    ans = solve(U, V)
    print(ans)