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:
u,v=map(int,input().split())
if v<u:
    print(-1)
elif u==v and u==0:
    print(0)
elif u==v:
    print(1)
    print(u)
else:
    if u%2==v%2:
    #    x=bin((v-u)//2+u)[2:][-1::-1]
      #  j=0
        if(((v-u)//2)+u)^((v-u)//2)==u:
            print(2)
            print((v-u)//2+u,(v-u)//2)
            
        else:
            print(3)
            print(u,(v-u)//2,(v-u)//2)
    else:
        print(-1)
        
##        st=1
##        stt=0
##        while st<=v*10:
##            if (u^st)+(((v-u)//2)^st)+((v-u)//2)==v:
##                stt=1
##                break
##            st*=2
##        
##        if(stt==1):
##            print(3)
##            print((u^st),(((v-u)//2)^st),((v-u)//2))
##        else:
##            print(u,u,u)
##