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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Rustam Musin (t.me/musin_acm)
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    DYekhabXORminator solver = new DYekhabXORminator();
    solver.solve(1, in, out);
    out.close();
  }

  static class DYekhabXORminator {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
      long needXor = in.readLong();
      long needSum = in.readLong();
      long[] ans = solve0(needXor, needSum);
      if (ans == null) {
        out.print(-1);
      } else {
        out.printLine(ans.length);
        out.print(ans);
//      System.err.println(check(ans, needXor, needSum));
      }
    }

    long[] solve0(long needXor, long needSum) {
      return compress(solve(needXor, needSum));
    }

    long[] solve(long needXor, long needSum) {
      if (needSum < needXor || ((needSum & 1) != (needXor & 1))) {
        return null;
      }
      if (needXor == needSum) {
        return new long[]{needXor};
      }
      long[] a = new long[3];
      a[0] = needXor;
      long haveSum = needXor;
      for (int i = 0; i < 62; i++) {
        if (getBit(haveSum, i) != getBit(needSum, i)) {
          a[1] |= 1L << (i - 1);
          a[2] |= 1L << (i - 1);
          haveSum += 1L << i;
        }
      }
      return a;
    }

    long[] compress(long[] a) {
      if (a == null) {
        return null;
      }
      int[] cnt = new int[64];
      for (long x : a) {
        long y = x;
        for (int i = 0; i < 64; i++, y >>= 1) {
          if ((y & 1) == 1) {
            cnt[i]++;
          }
        }
      }
      int max = 0;
      for (int x : cnt) {
        max = Math.max(max, x);
      }
      long[] res = new long[max];
      for (int i = 0; i < cnt.length; i++) {
        for (int j = 0; j < cnt[i]; j++) {
          res[j] |= 1L << i;
        }
      }
      return res;
    }

    int getBit(long x, int b) {
      return (int) ((x >> b) & 1);
    }

  }

  static class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private InputReader.SpaceCharFilter filter;

    public InputReader(InputStream stream) {
      this.stream = stream;
    }

    public int read() {
      if (numChars == -1) {
        throw new InputMismatchException();
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          throw new InputMismatchException();
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar++];
    }

    public long readLong() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      long res = 0;
      do {
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public boolean isSpaceChar(int c) {
      if (filter != null) {
        return filter.isSpaceChar(c);
      }
      return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
      public boolean isSpaceChar(int ch);

    }

  }

  static class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    public void print(long[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void close() {
      writer.close();
    }

    public void print(int i) {
      writer.print(i);
    }

    public void printLine(int i) {
      writer.println(i);
    }

  }
}