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 sys
 
def input():
    return sys.stdin.readline()
 
def iinput():
    return int(input())
 
def rinput():
    return input().split()
 
def rlinput():
    return [int(i) for i in input().split()]
 
def main():
    #q = rlinput() rinput() iinput() input()
    q = [0] * 100
    u, v = rlinput()
    if u <= v:
        if v == 0:
            print(0)
            return 0
        if v == u:
            print(1)
            print(v)
            return 0
        if (v - u) % 2 == 1:
            print(-1)
            return 0
        fl = True
        
        for i in range(70):
            if (v - u) & (1 << i):
                q[i - 1] += 1
                if u & (1 << (i - 1)):
                    fl = False
        w = [u, 0]
        
        if fl:
            for i in range(70):
                if q[i]:
                    w[1] += 1 << i
                    w[0] += 1 << i
        else:
            w.append(0)
            for i in range(70):
                if q[i]:
                    w[1] += 1 << i
                    w[2] += 1 << i  
                    
        print(len(w))
        print(*w)
        
    else:
        print(-1)
    
    
    
for i in range(1):
    main()