Problem: Now it's time of Olympiads. Vanya and Egor decided to make his own team to take part in a programming Olympiad. They've been best friends ever since primary school and hopefully, that can somehow help them in teamwork.

For each team Olympiad, Vanya takes his play cards with numbers. He takes only the cards containing numbers 1 and 0. The boys are very superstitious. They think that they can do well at the Olympiad if they begin with laying all the cards in a row so that:

  * there wouldn't be a pair of any side-adjacent cards with zeroes in a row; 
  * there wouldn't be a group of three consecutive cards containing numbers one. 



Today Vanya brought n cards with zeroes and m cards with numbers one. The number of cards was so much that the friends do not know how to put all those cards in the described way. Help them find the required arrangement of the cards or else tell the guys that it is impossible to arrange cards in such a way.

Input

The first line contains two integers: n (1 ≤ n ≤ 106) — the number of cards containing number 0; m (1 ≤ m ≤ 106) — the number of cards containing number 1.

Output

In a single line print the required sequence of zeroes and ones without any spaces. If such sequence is impossible to obtain, print -1.

Examples

Input

1 2


Output

101


Input

4 8


Output

110110110101


Input

4 10


Output

11011011011011


Input

1 5


Output

-1

Solution (in JAVA):

Solution:
import java.io.*;
public class Main {
    static InputReader in;
    static PrintWriter out;
    static StringBuilder sb;

    public static void main(String args[]) throws IOException {
        in = new InputReader();
        out = new PrintWriter(System.out);
        sb = new StringBuilder();
        int t = 1;
//        t = in.nextInt();
        while (t-- > 0) {
            solve();
        }
        out.print(sb);
        out.close();
    }


    private static void solve() throws IOException {
        int n = in.nextInt();
        int m = in.nextInt();
        String s = null;
        if (n == m) s = all(n, m, '0');
        if (s == null && n - m == 1) {
            s = '0' + all(n - 1, m, '0');
        }
        if (s == null && m - n == 1) {
            s = '1' + all(n - 1, m, '0');
        }
        if (s == null)
            s = zerosFirst(n, m);
        if (s == null) {
            s = onesFirst(n, m);
        }
        sb.append(s == null ? -1 : s);
    }

    private static String onesFirst(int n, int m) {
        if (m == 0) return null;
        StringBuilder ans = new StringBuilder();
        ans.append("1");
        int cntOnes = 1, rem1 = m - 1, rem0 = n;
        for (int i = 1; i < n + m; i++) {
            char back = ans.charAt(ans.length() - 1);
            if (rem0 == rem1) {
                ans.append(all(rem0, rem1, back));
                return ans.toString();
            }
            if (back == '0') {
                if (rem1 > 0 && cntOnes < 2) {
                    cntOnes++;
                    ans.append("1");
                    rem1--;
                } else return null;
            } else {
                if (rem1 > 0 && cntOnes < 2) {
                    cntOnes++;
                    ans.append("1");
                    rem1--;
                } else if (rem0 > 0) {
                    ans.append("0");
                    cntOnes = 0;
                    rem0--;
                } else return null;
            }
        }
        return String.valueOf(ans);
    }

    private static String all(int n, int m, char back) {
        StringBuilder ans = new StringBuilder();
        for (int i = 0; i < n + m; i++) {
            if (i % 2 == back - '0') {
                ans.append("1");
            } else {
                ans.append("0");
            }
        }
        return ans.toString();
    }

    private static String zerosFirst(int n, int m) {
        if (n == 0) return null;
        StringBuilder ans = new StringBuilder();
        int rem0 = n - 1, rem1 = m;
        ans.append("0");
        int cntOnes = 0;
        for (int i = 1; i < n + m; i++) {
            char back = ans.charAt(ans.length() - 1);
            if (back == '0') {
                if (rem1 > 0 && cntOnes < 2) {
                    cntOnes++;
                    ans.append("1");
                    rem1--;
                } else return null;
            } else {
                if (rem1 > 0 && cntOnes < 2) {
                    cntOnes++;
                    ans.append("1");
                    rem1--;
                } else if (rem0 > 0) {
                    ans.append("0");
                    cntOnes = 0;
                    rem0--;
                } else return null;
            }
        }
        return ans.toString();
    }

    static class InputReader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public InputReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public InputReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}