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 or u%2!=v%2:
    print(-1)
    exit()

if u==0 and v==0:
    print(0)
    exit()

if u==v:
    print(1)
    print(u)
    exit()

w = (v-u)//2
W = format(w, 'b')
U = format(u, 'b')
L = max(len(W), len(U))
W = '0'*(L-len(W))+W
U = '0'*(L-len(U))+U
a, b = 0, 0

for i in range(L):
    if W[i]=='1':
        if U[i]=='1':
            print(3)
            print(w, w, u)
            break
        else:
            a += 2**(L-1-i)
            b += 2**(L-1-i)
    else:
        if U[i]=='1':
            a += 2**(L-1-i)
else:
    print(2)
    print(a, b)