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:
#  =========     /\       /|    |====/|
#      |        /  \       |    |   / |
#      |       /____\      |    |  /  |
#      |      /      \     |    | /   |
#  ========= /        \  =====  |/====|  
#  code

# MOD = 998244353
# def pow(base , exp):
#     if exp == -1:
#         return pow(base , MOD - 2)
#     res = 1
#     base %= MOD
#     while exp > 0:
#         if exp % 2:
#             res = (res * base) % MOD
#         exp //= 2
#         base = (base * base) % MOD
    
#     res %= MOD
    #   return res

def main():
    u , v = map(int , input().split())
    if u == 0 and v == 0:
        print(0)
        return
    if u%2 != v%2 or  u > v:
        print(-1)
    elif u == v:
        print(1)
        print(u)
    else:
        x = (v - u)//2
        if x > 0:
            if u & x == 0:
                print(2)
                print(u ^ x , x)
            else:
                print(3)
                print(u,x,x)
        else:
            print(-1)
    return

if __name__ == "__main__":
    main()