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 sys import stdin, stdout

def main():
    a,b = list(map(int,stdin.readline().split()))
    if (a == 0):
        if b== 0:
            print ("0")
            return
        elif b % 2 == 0:
            print("2")
            print(str(int(b/2)) + " " + str(int(b/2)))
            return
        else:
            print("-1")
            return
    ans = []
    b -= a
    if (b == 0):
        print("1")
        print(a)
        return
    if b % 2 == 1 or b < 0:
        print("-1")
        return
    half = b>>1
    if half | a == half + a:
        print("2")
        print(half + a,half)
    else:
        print("3")
        print(half,half,a)
    
    
    
main()