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:
def calc():
    tot=2
    a=u
    b=0
    c=0
    d=v-u
    nb=0
    while(d > 0):
        if(d&1):
            if( (1<<(nb-1)) & a):
                tot=3
                b+=1<<(nb-1)
                c+=1<<(nb-1)
            else:
                a+=1<<(nb-1)
                b+=1<<(nb-1)
        d>>=1
        nb+=1
    return [a,b,c,tot]
u,v=map(int,input().split())
if(u==v and u==0):
    print(0)
    exit(0)
if(u > v):
    print(-1)
elif(u==v):
    print(1)
    print(u)
else:
    if((v-u)&1):
        print(-1)
    else:
        ans=calc()
        print(ans[-1])
        print(ans[0],ans[1],end=' ')
        if(ans[-1]==3):
            print(ans[2])