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.*;
import java.util.*;
import java.util.stream.Collectors;

public class Solution {

    public static void main(String[] args) throws IOException {
        IO io = new IO() ;
        int z = io.getInt(), o = io.getInt() ;
        StringBuilder res = new StringBuilder() ;

        if(!(o >= z - 1 && o <= 2*z + 2)){
            System.out.println(-1);
            return;
        }
        while(true){
            if(z == 0){
                res.append(1) ;
                o-- ;
            }
            else if(o == 0){
                res.append(0) ;
                z-- ;
            }
            else if(o < z){
                res.append(0) ;
                z-- ;
            }
            else if(o == z){
                res.append(1) ;
                res.append(0) ;
                o-- ; z-- ;
            }
            else{
                res.append("11") ;
                res.append("0") ;
                o -= 2 ; z-- ;
            }
            if(o == 0 && z == 0)
                break ;
        }
        System.out.println(res) ;
    }
}

class Utils {

    static int[][] fourDirs = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}} ;
    static int[][] eightDirs = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1}} ;

    public static List<Integer> sieve(int n){
        boolean b[] = new boolean[n + 1] ;
        List<Integer> ans = new ArrayList<>() ;
        Arrays.fill(b, true) ;

        for(int i = 2 ; i <= n ; i++){
            if(b[i]){
                ans.add(i) ;
                for(int j = i*i ; j >= 0 && j <= n ; j += i){
                    b[j] = false ;
                }
            }
        }
        return ans ;
    }

    public static boolean isPrime(long n){
        long sqrt = (long)Math.sqrt(n) ;
        for(int i = 2 ; i <= sqrt ; i++){
            if(n % i == 0)
                return false ;
        }
        return true ;
    }

    public static long mod(long n){
        if(n > 0)
            return n % 1000000007 ;
        return (n + 2000000014) % 1000000007 ;
    }

    public static boolean isSqr(long n){
        int sqrt = (int) Math.sqrt(n) ;
        return n == (long)sqrt*sqrt ;
    }

    public static Utils.Pair getSlope(int x0, int y0, int x1, int y1){
        int a = y1 - y0, b = x1 - x0, g = (int)Utils.gcd(Math.abs(a), Math.abs(b)) ;
        if(g != 0){
            a /= g ;
            b /= g ;
        }
        if(a < 0){
            a *= -1 ;
            b *= -1 ;
        }
        else if(a == 0){
            b = 1 ;
        }
        return new Utils.Pair(a, b) ;
    }

    public static boolean inRange(long i, long l, long h){
        return i >= l && i <= h ;
    }

    public static boolean isValid(int i, int j, int n, int m){
        return i >= 0 && j >= 0 && i < n && j < m ;
    }

    public static void swap(List<Integer> ls, int i, int j){
        int temp = ls.get(i) ;
        ls.set(i, ls.get(j)) ;
        ls.set(j, temp) ;
    }

    public static long gcd(long a, long b){
        if(a < b)
            return gcd(b, a) ;
        else if(a == b || b == 0)
            return a ;
        else{
            return gcd(b, a % b) ;
        }
    }

    public static long subSum(long[] pre, int l, int h){
        return l == 0 ? pre[h]: pre[h] - pre[l - 1] ;
    }

    public static class Pair implements Comparable<Pair>{
        public int l, h ;

        public Pair(int a, int b) {
            this.l = a;
            this.h = b;
        }

        @Override
        public int compareTo(Pair o) {
            return l - o.l ;
        }

        @Override
        public String toString() {
            return "Pair{" +
                    "l=" + l +
                    ", h=" + h +
                    '}';
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Pair pair = (Pair) o;

            if (l != pair.l) return false;
            return h == pair.h;
        }

        @Override
        public int hashCode() {
            int result = l;
            result = 31 * result + h;
            return result;
        }
    }

    public static void ifPrint(boolean test, Object ifValue, Object elseValue){
        System.out.println(test ? ifValue: elseValue) ;
    }

    public static void print(Character delim, Object... a){
        List<String> top = new ArrayList<>() ;
        for(Object aa: a)
            top.add(aa == null ? "null": aa.toString()) ;
        System.out.println(join(top, delim.toString())) ;
    }

    public static void print(Object... a){
        print(' ', a) ;
    }

    public static  <T extends Comparable<T>> int lowerBound(T[] arr, int l, int h, T key){
        while(l < h){
            int mid = (l + h) / 2 ;
            if(arr[mid].compareTo(key) < 0)
                l = mid + 1 ;
            else
                h = mid ;
        }
        return arr[l].compareTo(key) >= 0 ? l: -1 ;
    }

    public static <T extends Comparable<T>> int upperBound(T[] arr, int l, int h, T key){
        while(l < h){
            int mid = (l + h) / 2 ;
            if(arr[mid].compareTo(key) < 0)
                l = mid + 1 ;
            else if(arr[mid].compareTo(key) == 0)
                l = mid ;
            else
                h = mid ;
            if(h == l + 1)
                break ;
        }
        return arr[l].compareTo(key) >= 0 ? l: -1 ;
    }

    public static class IndexedElement<T> {
        int idx;
        T val;

        public IndexedElement(int idx, T val) {
            this.idx = idx;
            this.val = val;
        }

        @Override
        public String toString() {
            return "IndexedElement{" +
                    "idx=" + idx +
                    ", val=" + val +
                    '}';
        }
    }

    public static <T> ArrayList<IndexedElement<T>> getIndexedArray(List<T> ip) {
        ArrayList<IndexedElement<T>> op = new ArrayList<>();
        for (int i = 0; i < ip.size(); i++) {
            op.add(new IndexedElement<>(i, ip.get(i)));
        }
        return op;
    }

    public static <T> String join(List<T> ls) {
        return join(ls, " ") ;
    }

    public static <T> String join(List<T> ls, String delim) {
        StringJoiner sj = new StringJoiner(delim);
        for (T a : ls)
            sj.add(a.toString());
        return sj.toString();
    }

    public static <T> void print2DArray(List<List<T>> mat) {
        for (List<T> m : mat) {
            System.out.println("{ " + join(m, ", ") + " }");
        }
    }

    public static  <T> void reverseArrray(T[] arr, int l, int h){
        while(l < h){
            T temp = arr[l] ;
            arr[l] = arr[h] ;
            arr[h] = temp ;
            l++ ;
            h-- ;
        }
    }
}

class IO {
    private BufferedReader br = null;
    private StringTokenizer st = null;

    public IO() {
        this(System.in);
    }

    public IO(InputStream is) {
        this.br = new BufferedReader(new InputStreamReader(is));
    }

    public List<String> getStringArray(int n) throws IOException {
        if (n == 0)
            return new ArrayList<>();
        if (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        List<String> res = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            if (!st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            res.add(st.nextToken());
        }
        return res;
    }
    public String getString() throws IOException {
        List<String> res = this.getStringArray(1);
        return res.size() == 0 ? "" : res.get(0);
    }

    public List<Integer> getIntegerArray(int n) throws IOException {
        if (n == 0)
            return new ArrayList<>();
        List<String> res = getStringArray(n);
        return res.stream().map(Integer::parseInt).collect(Collectors.toList());
    }
    public Integer getInt() throws IOException {
        List<Integer> res = this.getIntegerArray(1);
        return res.size() == 0 ? 0 : res.get(0);
    }

    public List<Long> getLongArray(int n) throws IOException {
        if (n == 0)
            return new ArrayList<>();
        List<String> res = getStringArray(n);
        return res.stream().map(Long::parseLong).collect(Collectors.toList());
    }
    public Long getLong() throws IOException {
        List<Long> res = this.getLongArray(1);
        return res.size() == 0 ? 0L : res.get(0);
    }

    public List<Double> getDoubleArray(int n) throws IOException {
        if (n == 0)
            return new ArrayList<>();
        List<String> res = getStringArray(n);
        return res.stream().map(Double::parseDouble).collect(Collectors.toList());
    }
    public Double getDouble() throws IOException {
        List<Double> res = this.getDoubleArray(1);
        return res.size() == 0 ? 0.0 : res.get(0);
    }
}