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:

def main():
    
    u,v=readIntArr()
    ans=[]
    if u>v:
        ans.append([-1]) #impossible
    elif u==v:
        if u==0:
            ans.append([0])
        else:
            ans.append([1])
            ans.append([u])
    else:
        w=v-u
        if w%2==1:
            ans.append([-1]) #impossible because we need 2 of w/2 to xor-cancel each other out
        else:
            x=w//2
            #check if we can fit the set bits of x into u
            # (b&(1<<i))>0
            canFit=True
            i=0
            while 2**i<10**18:
                if (u&(1<<i))>0 and (x&(1<<i))>0: #clash
                    canFit=False
                i+=1
            if canFit==True:
                ans.append([2])
                ans.append([u|x,x])
            else:
                ans.append([3])
                ans.append([u,x,x])
    multiLineArrayOfArraysPrint(ans)
                
    
    return
    
#import sys
#input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
import sys
input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.
 
def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
 
inf=float('inf')
MOD=10**9+7

for _ in range(1):
    main()