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 E {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		long xor = sc.nextLong(), sum = sc.nextLong();
		int max = 63;
		int[] cnt = new int[max];
		boolean ok = true;
		for (int bit = 0; bit < max; bit++) {
			int x = (1L << bit & xor) == 0 ? 0 : 1;
			int s = (1L << bit & sum) == 0 ? 0 : 1;
			if (x == 1 && s == 1) {
				cnt[bit]++;
			} else if (x == 0 && s == 1) {
				if (bit == 0) {
					ok = false;
					break;
				}
				cnt[bit - 1] += 2;
			} else if (x == 1 && s == 0) {
				if (bit == 0) {
					ok = false;
					break;
				}
				cnt[bit - 1] += 2;
				cnt[bit]++;
				sum -= (2L << bit);
				if (sum < 0) {
					ok = false;
					break;
				}
			}

		}
		if (!ok) {
			System.out.println(-1);
			return;
		}
		int len = 0;
		for (int x : cnt)
			len = Math.max(len, x);
		out.println(len);
		long[] ans = new long[len];
		for (int bit = 0; bit < max; bit++) {
			for (int i = 0; i < cnt[bit]; i++)
				ans[i] |= 1L << bit;

		}
		for (long x : ans)
			out.print(x + " ");
		out.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		Scanner(String fileName) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(fileName));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}

		boolean ready() throws IOException {
			return br.ready();
		}

		int[] nxtArr(int n) throws IOException {
			int[] ans = new int[n];
			for (int i = 0; i < n; i++)
				ans[i] = nextInt();
			return ans;
		}

	}

	static void sort(int[] a) {
		shuffle(a);
		Arrays.sort(a);
	}

	static void shuffle(int[] a) {
		int n = a.length;
		Random rand = new Random();
		for (int i = 0; i < n; i++) {
			int tmpIdx = rand.nextInt(n);
			int tmp = a[i];
			a[i] = a[tmpIdx];
			a[tmpIdx] = tmp;
		}
	}

}