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:
# https://www.geeksforgeeks.org/find-two-numbers-sum-xor/

x,s = map(int,input().split())
if x == s == 0:
    print(x)
elif x == s:
    print(1)
    print(x)
elif x > s or (s-x)%2:
    print(-1)
else:
    def check(s,x):
        a = (s-x)//2
        aa,bb = 0,0
        for i in range(0,64):
            xi = x & (1 << i)
            ai = a & (1 << i)
            if xi == 0 and ai == 0:
                pass
            elif xi == 0 and ai > 0:
                aa = (1 << i) | aa
                bb = (1 << i) | bb
            elif xi > 0 and ai == 0:
                aa = (1 << i) | aa
            else:
                return [x,a,a]
        return [aa,bb]
    print(len(check(s,x)))
    print(*check(s,x))