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:


def run():
    xo, s = list(map(int, input().split()))
    if s < xo:
        print(-1)
        return
    if s == xo:
        if s != 0:
            print(1)
        print(xo)
        return
    if (s - xo) % 2 != 0:
        print(-1)
        return 
    an = (s - xo) // 2 
    an_binary = "{0:b}".format(an)
    xo_binary = "{0:b}".format(xo)
    xo_binary = xo_binary.rjust(len(an_binary), "0")
    an_binary = an_binary.rjust(len(xo_binary), "0")

    include_c = False
    for i in range(len(xo_binary)):
        if an_binary[i] == "1" and xo_binary[i] == "1":
           include_c = True
           break

    # for i in range(len(xo_binary)):
    #     if include_c:
    #         if an_binary[i] == "1":
    #             a += "1"
    #             b += "1"
    #             c += "1"
    #         else:
    #             if xo_binary[i] == "1":
    #                 a += "1"
    #                 b += "0"
    #                 c += "0"
    #             else:
    #                 a += "0"
    #                 b += "0"
    #                 c += "0"

    #     else:
    #         if an_binary[i] == "1":
    #             a += "1"
    #             b += "1"
    #         elif xo_binary[i] == "1":
    #             a += "1"
    #             b += "0"
    #         else:
    #             a += "0"
    #             b += "0"
    
    if not include_c:
        a = xo + an
        b = an
        print(2)
        print(str(a) + " " + str(b))
    else:
        a = xo
        b = an
        print(3)
        print(str(a) + " " + str(b) + " " + str(b))

if __name__ == "__main__":
    run()