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:
from math import *


ap = [0] * 100

def check(x, te, a):
    n = len(a)
    ti = ceil(log(te, 2))
    #print(ti, te)
    ta = [0]*n
    while te > 0 and ti >= 0:
        if ti < len(a):         
            tx = x
            if a[ti]:
                tx -= 1
            tx //= 2
            #print(tx, ti)
            while te > 0 and tx > 0 and te >= ap[ti]:
                te -= ap[ti]
                tx -= 1
                ta[ti] += 1
        #print(ti, te, ap[ti])
        
        ti -= 1
    #print(te, x, a, ta)
    if te == 0:
        return [True, ta]
    else:
        return [False]
    

u, v = map(int, input().split())
if u > v:
    print(-1)
elif u == v:
    if u == 0:
        print(0)
    else:
        print(1)
        print(u)
else:
    a = [int(i) for i in bin(u)[2:]]
    a.reverse()
    a += (len(bin(v)) - len(bin(u)))*[0]
    #print(a)
    n = len(a)
    cp = 1
    ts = 0
    for i in range(n):
        if a[i]:
            ts += cp
        ap[i] = cp
        cp *= 2
    te = (v - ts)
    if te % 2 == 1:
        print(-1)
    else:
        te //= 2
        b = a[:]
        tb = 1 if 1 in a else 0
        lb = tb
        ub = 10*n
        while lb + 1 < ub:
            tx = (ub + lb) // 2
            dx = (ub - lb) // 2
            if check(tx, te, a)[0]:
                ub -= dx
            else:
                lb += dx
            #print(lb, ub)
        tx = (ub + lb) // 2
        for i in range(3):
            if tx > tb and check(tx-1, te, a)[0]:
                tx -= 1
            elif not check(tx, te, a)[0]:
                tx += 1
        t2 = check(tx, te, a)[1]
        for i in range(n):
            a[i] += 2*t2[i]
        tans = []
        while(sum(a)) > 0:
            tn = 0
            for i in range(n):
                if a[i] > 0:
                    tn += ap[i]
                    a[i] -= 1
            tans.append(tn)
        print(len(tans))
        print(' '.join(map(str, tans)))