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 JAVA):

Solution:
import java.io.*;
import java.util.*;

public class XORsist_round628 {
    public static void main(String s[]) throws Exception {
        Reader r = new Reader();
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        long u=r.nextLong();
        long v=r.nextLong();
        long uc=u;
        long vc=v;
        if(u>v || (u%2!=v%2))
            System.out.println("-1");
        else if(u==v){
            if(u==0)
                System.out.println("0");
            else System.out.println(1+"\n"+u);
        }else if(u==0)
            System.out.println("2\n"+(v/2)+" "+(v/2));
        else {
            boolean flag=true;
            long w=(v-u)/2;
            long wc=w;
            long res1=0;
            long res2=0;
            int count=0;
            while(w!=u ||(w!=0)){
//                System.out.println("w="+Long.toBinaryString(w));
//                System.out.println("u="+Long.toBinaryString(u));
//                System.out.println("v="+Long.toBinaryString(v));

                int a=(int)w%2;
                int b=(int)u%2;
                if(a==0 && b==1){
                    res1=res1|(1<<count);
                }else if(a==1 && b==0){
                    res1=(res1|(1<<count));
                    res2=res2|(1<<count);
                }else if(a==1 && b==1){
                    flag=false;
                    break;
                }
                u=u>>1;
                w=w>>1;
                count++;
            }
            if(flag){
                System.out.println("2");
                System.out.println(uc+wc+" "+wc);
            }else {
                System.out.println("3");
                System.out.println(wc+" "+wc+" "+uc);
            }
        }
    }

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}