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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.Scanner;
import java.util.StringTokenizer;

public class D {
	
	public static void main(String[] args) throws Exception
	{
		new D().run();
	}
	
	public void genCase() throws IOException
	{
		while(true)
		{
			long time = System.currentTimeMillis();
			long a = (long)(Math.random() * Long.MAX_VALUE);
			long b = (long)(Math.random() * Long.MAX_VALUE);
			System.out.print(a+" "+b+" ");
			int ans = run(a, b);
			if(ans > 3)
			{
				System.out.println("BAD");
				new Scanner(System.in).nextLine();
			}
			System.out.println(ans+" "+(System.currentTimeMillis() - time));
		}
	}
	
	public int run(long xor, long sum) throws IOException
	{
		BufferedReader file = new BufferedReader(new InputStreamReader(System.in));
		//StringTokenizer st = new StringTokenizer(file.readLine());
		//long xor = Long.parseLong(st.nextToken());
		//long sum = Long.parseLong(st.nextToken());
		if((xor & 1) != (sum & 1) || xor > sum)
		{
			return -1;
		}
		String addBits = Long.toBinaryString(sum);
		String xorBits = Long.toBinaryString(xor);
		while(xorBits.length() < addBits.length())
			xorBits = "0"+xorBits;
		char[] bits = xorBits.toCharArray();
		
		int[] assignments = new int[bits.length];
		BigInteger tot = BigInteger.ZERO;
		BigInteger one = BigInteger.ONE;
		for(int i = 0;i<bits.length;i++)
		{

			if(bits[i] == '1')
			{
				assignments[i]++;
				tot = tot.add(one.shiftLeft(bits.length - i - 1));
				//tot += (1l << (bits.length - i - 1));
			}
			while(tot.add(one.shiftLeft(bits.length - i)).compareTo(BigInteger.valueOf(sum))<=0)//tot + (1l << (bits.length - i)) <= sum)
			{
				assignments[i]+=2;
				tot = tot.add(one.shiftLeft(bits.length - i));
			}
		}
		int max = 0;
		for(int x: assignments)
		{
			max = Math.max(max, x);
		}
		if(max == 0)
		{
			//System.out.println(0);
			return 0;
		}
		return max;
		//System.out.println(max);
		/*for(int i = 0;i<max;i++)
		{
			long curr = 0;
			for(int j = 0;j < assignments.length;j++)
			{
				curr *=2;
				if(assignments[j] != 0)
				{
					curr++;
					assignments[j]--;
				}
			}
			//System.out.print(curr+" ");
		}*/
	}

//7721136790713220096 2937084422204473344

	public void run() throws Exception
	{
		BufferedReader file = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(file.readLine());
		long xor = Long.parseLong(st.nextToken());
		long sum = Long.parseLong(st.nextToken());
		if((xor & 1) != (sum & 1) || xor > sum)
		{
			System.out.println(-1);
			return;
		}
		String addBits = Long.toBinaryString(sum);
		String xorBits = Long.toBinaryString(xor);
		while(xorBits.length() < addBits.length())
			xorBits = "0"+xorBits;
		char[] bits = xorBits.toCharArray();
		
		int[] assignments = new int[bits.length];
		BigInteger tot = BigInteger.ZERO;
		BigInteger one = BigInteger.ONE;
		for(int i = 0;i<bits.length;i++)
		{
			//System.out.println(i+" "+tot);
			if(bits[i] == '1')
			{
				assignments[i]++;
				tot = tot.add(one.shiftLeft(bits.length - i - 1));
				//tot += (1l << (bits.length - i - 1));
			}
			while(tot.add(one.shiftLeft(bits.length - i)).add(getRemaining(i, bits)).compareTo(BigInteger.valueOf(sum))<=0)//tot + (1l << (bits.length - i)) <= sum)
			{
				assignments[i]+=2;
				tot = tot.add(one.shiftLeft(bits.length - i));
			}
		}
		int max = 0;
		for(int x: assignments)
		{
			max = Math.max(max, x);
		}
		if(max == 0)
		{
			System.out.println(0);
			return;
		}
		System.out.println(max);
		for(int i = 0;i<max;i++)
		{
			long curr = 0;
			for(int j = 0;j < assignments.length;j++)
			{
				curr *=2;
				if(assignments[j] != 0)
				{
					curr++;
					assignments[j]--;
				}
			}
			System.out.print(curr+" ");
		}
		
	}
	
	public BigInteger getRemaining(int i, char[] bits)
	{
		BigInteger ans = BigInteger.ZERO;
		for(int j = i+1;j<bits.length;j++)
		{
			ans = ans.multiply(BigInteger.valueOf(2));
			if(bits[j] == '1')
			{
				ans = ans.add(BigInteger.ONE);
			}
		}
		return ans;
	}
	
	
}