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:
xor,sm=map(int,input().split())
if(xor>sm):
    print("-1")
elif(xor%2 != sm%2):
    print("-1")
elif(xor==0 and sm==0):
    print("0")
elif(xor==0):
    print("2")
    v=sm//2
    print(v,v)
elif(xor==1 and sm==1):
    print("1")
    print("1")
elif(xor==sm):
    print("1")
    print(xor)
else:
    val=sm-xor
    val//=2
    AND=val
    a=0
    b=0
    bl=True
    for i in range(64):
        x1=(xor & (1<<i))
        and2=(AND & (1<<i))
        if(x1==0 and and2==0):
            continue
        elif(x1==0 and and2>0):
            a=(1<<i)|a
            b=(1<<i)|b
        elif(x1>0 and and2==0):
            a=((1<<i)|a)
        else:
            bl=False
            break
    if(bl==True):
        print("2")
        print(a,b)
    else:
        print("3")
        print(val,val,xor)