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

def fun(u,v):
    x=[0]*64
    z=(v-u)//2
    
    a=list(bin(u)[2:])
    # print(a)
    aa=len(a)
    for i in range(aa):
        if(a[aa-i-1]=='1'):
            x[i]+=1
    a=list(bin(z)[2:])
    aa=len(a)
    for i in range(aa):
        if(a[aa-i-1]=='1'):
            x[i]+=2
    # print(x)
    xxx=max(x)
    op=[]
    for i in range(xxx):
        a=0
        for j in range(64):
            if(x[j]):
                x[j]-=1
                a+=2**j
        op.append(a)
    print(len(op))
    print(*op)
    # return 1
    
    
a,b=list(map(int,sys.stdin.readline().strip().split()))
u,v=a,b
if(a>b):
    print(-1)
else:
    if(u%2==1):
        if(v%2==1):
            # print(fun(u,v))
            fun(u,v)
        else:
            print(-1)
    else:
        if(v%2==0):
            # print(fun(u,v))
            fun(u,v)
        else:
            print(-1)