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:
# max array length is 3

import math
u , v = [int(x) for x in input().split()]
x = v-u
arr = []

def check(u , x):
    # check if they have nothing in common
    if u!=0:
        bits = int(math.log2(u))
    else:
        bits = 0
    for i in range(0 , bits+2):
        if (1<<i) & u!=0:
            if (1<<i) & x!=0:
                return False
    return True

if x<0 or x%2==1:
    print(-1)
else:
    if check(u , x//2):
        u = u^(x//2)
    else:
        arr.append(x//2)
    if x//2!=0:
        arr.append(x//2)
    if u!=0:
        arr.append(u)
    print(len(arr))
    for i in range(0 , len(arr)):
        print(int(arr[i]) , end=' ')