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 main():
    u0, v = map(int, input().split())
    if u0 > v or (v - u0) % 2 != 0:
        print(-1)
        return 0;
    
    u = [0 for i in range(100)]
    curr = 0
    while (u0 > 0):
        u[curr] = u0 % 2
        u0 //= 2
        curr += 1
    
    out = [0 for i in range(100)]
    s = 0
    for i in range(99, -1, -1):
        if (u[i]):
            s += (1 << i);
            out[0] += (1 << i);
    for i in range(99, -1, -1):
        cnt = 0
        if (u[i]):
            cnt = 1;
        while s + (1 << (i + 1)) <= v:
            s += (1 << (i + 1))
            out[cnt] += (1 << i)
            out[cnt + 1] += (1 << i)
            cnt += 2;
    if (s != v):
        print(-1)
        return 0
    ans = 0
    for i in range(0, 100):
        ans += (out[i] != 0)
    print(ans)
    for i in range(0, 100):
        if (out[i] == 0):
            break
        print(out[i], end = ' ');

main()