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.util.Arrays;
import java.util.Scanner;

public class testMemory {
	static Scanner sc =new Scanner(System.in);
	public static boolean check(int x,int y) {
		    if(y==(x+1)||y==(x-1))
		        return true;
		    else
		        return false;
	}
	
	public static void run() {
		int k=sc.nextInt();
		int key[]=new int[k];
		for(int i=0;i<k;i++)
			key[i]=sc.nextInt();
		//Arrays.sort(key);
		int l=sc.nextInt();
		int lock[]=new int[l];
		for(int i=0;i<l;i++)
			lock[i]=sc.nextInt();
		//Arrays.sort(lock);

	//	int j=0;
		for(int i=0;i<k;i++) {
           for(int j=0;j<l;j++) {
        	   if(check(key[i],lock[j]))
        		   System.out.println(key[i]);
        	   return;
           }
		}
	}
	
	public static void EhabTheXorcist() {
		long u=sc.nextLong();
		long v=sc.nextLong();
		if(v<u) {
			System.out.println(-1);
			return;
		}
		if(u==0&&v==0) {
			System.out.println(0);
			return;
		}
			
		if(u==v) {
			System.out.println(1);
			System.out.println(u);
			return;
		}
		if((u&1)!=0&&(v&1)==0) {
			System.out.println(-1);
			return;
		}
		if((u&1)==0&&(v&1)!=0) {
			System.out.println(-1);
			return;
		}
		long x=(v>>1)-(u>>1);
		if(u==0) {
			System.out.println(2);
			System.out.println(x+" "+x);
			return;
		}
		long l=u;
		long r=v;
		while(l < r) {
			//System.out.println(l+"    "+r);
			long m = (l>>1)+(r>>1);
			long t=m^u;
			long s=t+m;
			//System.out.println("m "+m+" t "+t);
			if(s==v) {
				System.out.println(2);
				System.out.println(m+" "+t);
				return;
			}
			else if(s>v) {
				r=m-1;
			}
			else {
				l=m+1;
			}
		}
		if(l==r) {
			if((l^r)==u&&l+r==v) {
				System.out.println(2);
				System.out.println(l+" "+r);
				return;
			}
		}
		System.out.println(3);
		System.out.println(u+" "+x+" "+x);
		
		
		
		
		
	}
	

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		//run();
		EhabTheXorcist();

	}

}