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.*;

/**
 * A simple template for competitive programming problems.
 */
public class Solution {
    //final InputReader in = new InputReader("input.txt");
    final InputReader in = new InputReader(System.in);

    final PrintWriter out = new PrintWriter(System.out);

    void solve() {
        long u = in.nextLong();
        long v = in.nextLong();
        int[] ans = new int[64];

        if(v<u) {
            out.println(-1);
            return;
        }

        int i = 0;
        boolean elde = false;
        while(v>0) {
            boolean isV = (v&1L)==1L;
            boolean isU = (u&1L)==1L;

            if(isV && isU) {
                if(!elde) {
                    ans[i]++;
                } else {
                    ans[i]++;
                    ans[i-1] += 2;
                }
            } else if(isV && !isU) {
                if(elde) {
                    elde = false;
                } else {
                    if(i==0) {
                        out.println(-1);
                        return;
                    }
                    ans[i-1] += 2;
                }
            } else if(!isV && isU) {
                if (elde) {
                    ans[i]++;
                } else {
                    if(i==0) {
                        out.println(-1);
                        return;
                    }
                    ans[i]++; 
                    ans[i-1]+=2;
                    elde = true;
                }
            } else if(!isV && !isU) {
                if(elde) {
                    ans[i-1] += 2;
                }
            }

            i++;
            v >>= 1;
            u >>= 1;
        }

        if(elde) {
            out.println(-1);
            return;
        }

        long[] ca = createArray(ans);

        out.println(ca.length);

        for(int j=0; j<ca.length; j++) {
            out.print(ca[j] + " ");
        }
        out.println();
    }

    long[] createArray(int[] counts) {
        int max = 0;
        for(int i=0; i<counts.length; i++) {
            max = Math.max(counts[i], max);
        }

        long[] ret = new long[max];

        for(int i=0; i<max; i++) {
            long num = 0L;
            for(int j=0; j<counts.length; j++) {
                if(counts[j]>0) {
                    counts[j]--;
                    num |= (1L<<j);
                }
            }
            ret[i] = num;
        }

        return ret;
    }
    public static void main(String[] args) throws FileNotFoundException {
        Solution s = new Solution();
        Long t1 = System.currentTimeMillis();
        s.solve();
        System.err.println(System.currentTimeMillis() - t1 + " ms");
        s.out.close();
    }

    public Solution() throws FileNotFoundException {
    }

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

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

        InputReader(String fileName) {
            InputStream stream = null;
            try {
                stream = new FileInputStream(fileName);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            this.stream = stream;
        }

        int[] nextArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextInt();
            return arr;
        }

        int[][] nextMatrix(int n, int m) {
            int[][] matrix = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    matrix[i][j] = nextInt();
            return matrix;
        }

        String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        long nextLong() {
            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;
        }

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

        double nextDouble() {
            return Double.parseDouble(nextString());
        }

        private 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++];
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }

}