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 math import gcd
import sys


def input():
    return sys.stdin.readline().rstrip()


def slv():
    u, v = map(int, input().split())
    if u > v:
        print(-1)
        return
    if (v - u) % 2 != 0:
        print(-1)
        return

    # 0 <= L <= 3

    #L = 0 or L == 1
    if u == v:
        if u > 0:
            print(1)
            print(u)
        elif u == 0:
            print(0)
        return
    else:
        #L = 2
        d = (v - u) >> 1
        flag = True
        x, y = 0, 0
        for i in range(100):
            if (d >> i) & 1:
                if (u >> i) & 1:
                    flag = False
                    break
                else:
                    x += (1 << i)
                    y += (1 << i)

            else:
                if (u >> i) & 1:
                    x += (1 << i)
                    y += 0
        if flag:
            array = [x, y]
            assert (x ^ y == u and x + y == v)
            print(2)
            print(*array)
            return

    x, y, z = u, 0, 0
    d = (v - u) >> 1
    for i in range(100):
        if (d >> i) & 1:
            y += (1 << i)
            z += (1 << i)
    assert (x ^ y ^ z == u and x + y + z == v)
    print(3)
    array = [x, y, z]
    print(*array)
    return


def main():
    #t = int(input())
    t = 1
    for _ in range(t):
        slv()
    return


if __name__ == "__main__":
    # in_txt = open("in.txt", "r")
    # out_txt = open("out.txt", "w")
    # sys.stdin = in_txt
    # sys.stdout = out_txt
    main()