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
import math
input=sys.stdin.readline
#t=int(input())
t=1
for _ in range(t):
    #n=int(input())
    u,v=map(int,input().split())
    #a=list(map(int,input().split()))
   
    if (u+v)%2!=0 or u>v:
        print(-1)
    else:
        if u==v and u==0:
            print(u)
        elif u==v:    
            print(1)
            print(u)
        else:
            an=(v-u)//2
            a=0
            b=0
            ch=1
            for i in range(60):
                #print((1<<i),an & (1<<i),an,(u & (1<<i)),u)
                if  (an & (1<<i))>0 and (u & (1<<i))==0:
                    a=a |(1<<i)
                    b= b|(1<<i)
                if   (an & (1<<i))>0 and (u & (1<<i))>0:  
                    ch=0
                    break                
                if (an & (1<<i))==0 and (u & (1<<i))>0:
                    a=a|(1<<i)
            if ch==0:
                print(3)
                print(u,an,an)
            else:
                print(2)
                print(a,b)