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.util.*;
import java.io.*;

public class AiseHi {
	static class FastReader
	{
	BufferedReader br;
	StringTokenizer st;

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

	String next()
	{
	while (st == null || !st.hasMoreElements())
	{
	try
	{
	st = new StringTokenizer(br.readLine());
	}
	catch (IOException e)
	{
	e.printStackTrace();
	}
	}
	return st.nextToken();
	}

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

	long nextLong()
	{
	return Long.parseLong(next());
	}

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

	String nextLine()
	{
	String str = "";
	try
	{
	str = br.readLine();
	}
	catch (IOException e)
	{
	e.printStackTrace();
	}
	return str;
	}
	}
	static int m = (int)(1e9+7);
	static long mod(long x) {
		return ((x%m + m)%m);
	}
	static long add(long a,long b) {
		return mod(mod(a)+mod(b));
	}
	static long mul(long a,long b) {
		return mod(mod(a) * mod(b));
	}
	public static void main (String[] args) {
		FastReader sc = new FastReader();
		int t = 1;
//		t = sc.nextInt();
		while(t-->0) {
			int n = sc.nextInt();
			int m = sc.nextInt();
			
			if(n>m && n-m>1) {
				System.out.println(-1);
				return;
			}
			if(m>n ) {
				int temp = m;
				if(temp%2==0) temp/=2;
				else temp = temp/2 + 1;
				if(temp-n>1) {
					System.out.println(-1);
					return;
				}
			}
			StringBuilder st = new StringBuilder();
			if(n>=m) {
				
				int z = 0;
				if(n==m) z = (n+m)/2;
				else z = (n+m-1)/2;
				for(int i=0;i<z;i++) {
					st.append("01");					
				}					
				if(n-m==1)
				st.append("0");
				if(m-n==1)
					st.append("1");
				
			}
			else {
				while(m>0) {
					if(n==0) {
						if(m==2) {
							st.append("11");
							m-=2;
						}
						else {
							st.append("1");
							m--;
						}
					}
				    else if(m-n>1) {
						st.append("110");
						m-=2;
						n--;
					}
					else {
						st.append("10");
						m--;n--;
					}
				}
			}
			System.out.println(st);
		}
	}
	private static void swap(int[] a, int i, int j) {
		int temp = a[i];
		a[i] = a[j];
		a[j] = temp;
	}
	static long lstbt(long val) {
		long msk = val & (val-1);
		return (long) (Math.log(val^msk)/Math.log(2));
	}
	private static long sqrt(long x) {
		long l = 1,h = x;
		long ans = 0;
		while(l<=h) {
			long mid = (l+(h-l)/2);
			if(mid>x/mid) h = mid-1;
			else {
				ans = mid;
				l = mid+1;
			}
		}
		return ans;
	}
	static boolean prime[] = new boolean[10000001];
	static void sieve() {
		prime[0] = true;
		prime[1] = true;
		int max = 10000000;
		for(int i=2;i*i<=max;i++) {
			if(!prime[i]) {
				for(int j=i*i;j<=max;j+=i)
					prime[j] = true;
			}
		}
	}
	static String reverse(String x) {
		StringBuilder input1 = new StringBuilder();
		
        input1.append(x);
        
        input1 = input1.reverse();
        
        return input1.toString();
	}
	static int gcd(int val, int g) {
		if(g==0) return val;
		
		return gcd(g,val%g);
	}
}
class pair implements Comparable<pair>{
	long a;
	long b;
	pair(long a,long b){
		this.a = a;
		this.b = b;
	}
	@Override
	public int compareTo(pair o) {
		// TODO Auto-generated method stub
		return (int) ((2*this.a+this.b)- (2*o.a+o.b)) ;
	}
}