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 u==v and u==0 :
    print(0)
else :
    if v<u or (v-u)%2==1 :
        print(-1)
    else :
        if u==v :
            print(1)
            print(u)
        else :
            ub=[]
            a1=u
            while u>0 :
                ub.append(u%2)
                u=u//2 
            vb=[]
            v=(v-a1)//2
            a2=v
            while v>0 :
                vb.append(v%2)
                v=v//2 
            # print(ub,vb)
            flag=0 
            for i in range (min(len(ub),len(vb))) :
                if ub[i]==vb[i] and ub[i]==1 :
                    flag=1 
                    break
            if flag==1 :
                print(3)
                print(a1,a2,a2)
            else :
                print(2)
                print(a1+a2,a2)