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:
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

# ------------------- fast io --------------------
def compute(S, X):
    A = (S - X) // 2
    a = 0
    b = 0

    # Traverse through all bits
    for i in range(64):
        Xi = (X & (1 << i))
        Ai = (A & (1 << i))
        if (Xi == 0 and Ai == 0):
            # Let us leave bits as 0.
            pass

        elif (Xi == 0 and Ai > 0):
            a = ((1 << i) | a)
            b = ((1 << i) | b)

        elif (Xi > 0 and Ai == 0):
            a = ((1 << i) | a)
            # We leave i-th bit of b as 0.

        else:  # (Xi == 1 and Ai == 1)
            return -1

    return [a, b]

x, y = map(int, input().split())

if y == 0 and x == 0:
    print(0)
    quit()

if y == 0:
    print(-1)
    quit()

if x == 0:
    if y % 2 == 0:
        print(2)
        print(y // 2, y // 2)
        quit()
    else:
        print(-1)
        quit()


if x == y:
    print(1)
    print(x)
    quit()

if x > y:
    print(-1)
    quit()

diff = y - x

if diff % 2 == 0:
    ans = compute(y, x)
    if ans != -1:
        print(2)
        print(ans[0], ans[1])
    else:
        print(3)
        print(x, diff//2, diff//2)

else:
    print(-1)