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,os,io
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

u,v = [int(i) for i in input().split()]
if u>v or (v-u)%2:
    print(-1)
elif u==v==0:
    print(0)
elif u==v:
    print(1)
    print(u)
else:
    ans = []
    b = bin(u)[2:][::-1]
    diff = v-u
    diff= diff//2
    bd = bin(diff)[2:][::-1]
    flag = 0
    for i in range (min(len(b),len(bd))):
        if b[i]=='1' and bd[i]=='1':
            print(3)
            print(u,diff,diff)
            flag = 1
            break
    if flag == 0:
        print(2)
        print(u+diff, diff)