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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
string Ternary_representation = "";
bool visited[1];
long long mod = 1e9 + 7;
bool isVowel(char c) {
  if (c != 'a' && c != 'o' && c != 'u' && c != 'e' && c != 'i') {
    return false;
  } else {
    return true;
  }
}
bool isConst(char c) {
  if (c != 'a' && c != 'o' && c != 'u' && c != 'e' && c != 'i') {
    return true;
  } else {
    return false;
  }
}
bool cmp_x(pair<long long, long long> a, pair<long long, long long> b) {
  if (a.first == b.first) {
    return a.second < b.second;
  }
  return a.first < b.first;
}
bool cmp_y(pair<int, int> a, pair<int, int> b) {
  if (a.second == b.second) {
    return a.first < b.first;
  }
  return a.second < b.second;
}
bool cmp(int a, int b) { return abs(a) > abs(b); }
bool sort_by_third(pair<pair<long long, long long>, long long> a,
                   pair<pair<long long, long long>, long long> b) {
  return a.second > b.second;
}
bool isprime(int n) {
  if (n == 1) {
    return false;
  }
  if (n <= 3) {
    return true;
  }
  if (n % 2 == 0) {
    return false;
  }
  if (n % 3 == 0) {
    return false;
  }
  for (int i = 5; i * i <= n; i += 4) {
    if (n % i == 0) {
      return false;
    }
    if (n % (i + 2) == 0) {
      return false;
    }
  }
  return true;
}
bool isThere(vector<pair<int, int> > arr, pair<int, int> x, long long left,
             long long right) {
  if (left > right) {
    return false;
  }
  long long mid = (left + right) / 2;
  if (arr[mid] < x) {
    return isThere(arr, x, mid + 1, right);
  }
  if (arr[mid] > x) {
    return isThere(arr, x, left, mid - 1);
  }
  if (arr[mid] == x) {
    return true;
  }
  return false;
}
long long binarySearch(long long arr[], long long x, int size) {
  long long left = 0, right = size - 1;
  while (left <= right) {
    long long mid = (left + right) / 2;
    if (arr[mid] > x) {
      right = mid - 1;
    } else {
      left = mid + 1;
    }
  }
  return left;
}
long long power(long long a, long long b) {
  if (b == 0) {
    return 1;
  }
  long long ret = power(a, b / 2);
  ret *= ret;
  if (b & 1) {
    ret *= a;
  }
  return ret;
}
bool sort_strings_by_size(string a, string b) { return a.size() < b.size(); }
long long gcd(long long a, long long b) {
  if (a > b) {
    long long mmry = a;
    a = b;
    b = mmry;
  }
  if (a == 0) {
    return b;
  }
  gcd(a, b % a);
}
void init_toTernary(unsigned long long n) {
  if (n == 0) {
    return;
  }
  char x = (n % 3) + '0';
  Ternary_representation += x;
  n /= 3;
  init_toTernary(n);
  return;
}
void toTernary(unsigned long long n) {
  init_toTernary(n);
  reverse(Ternary_representation.begin(), Ternary_representation.end());
}
class Stack {
  vector<int> n;

 public:
  Stack() {}
  void push(int a);
  void pop();
  int size();
  bool isempty();
  int front();
};
void Stack::push(int a) {
  n.push_back(a);
  return;
}
void Stack::pop() {
  n.pop_back();
  return;
}
int Stack::size() { return n.size(); }
bool Stack::isempty() {
  if (n.size() == 0) {
    return true;
  } else {
    return false;
  }
}
int Stack::front() { return n[n.size() - 1]; }
class Graph {
  int numberOfVertices;
  vector<vector<int> > adjacencyList;
  int dfss(int s, long long arr[]) {
    visited[s] = true;
    long long ret = arr[s];
    for (int u = 0; u < adjacencyList[s].size(); u++) {
      if (!visited[adjacencyList[s][u]]) {
        ret = min(1ll * dfss(adjacencyList[s][u], arr), ret);
      }
    }
    return ret;
  }

 public:
  Graph(long long v) : numberOfVertices(v), adjacencyList(v) {}
  void insertEdge(int u, int v);
  vector<int> show(int v);
  void resize(int v);
  long long dfs(long long arr[]);
};
void Graph::insertEdge(int u, int v) {
  adjacencyList[u].push_back(v);
  return;
}
vector<int> Graph::show(int v) { return adjacencyList[v]; }
void Graph::resize(int v) {
  adjacencyList.resize(v);
  numberOfVertices = v;
}
long long Graph::dfs(long long arr[]) {
  long long cnt = 0;
  for (int i = 0; i < numberOfVertices; i++) {
    if (!visited[i]) cnt += dfss(i, arr);
  }
  return cnt;
}
int main() {
  int n, m;
  cin >> n >> m;
  if (n >= m + 2) {
    cout << -1;
  } else if (m > (2 * n) + 2) {
    cout << -1;
  } else {
    if (n - 1 == m) {
      cout << 0;
      for (long long i = 1; i < n + m; i += 2) {
        cout << 10;
      }
    } else if (n == m) {
      for (long long i = 0; i < n + m; i += 2) {
        cout << 10;
      }
    } else {
      for (long long i = 0; i < min(n, m - n); i += 1) {
        cout << 110;
      }
      if (m <= 2 * n) {
        for (long long i = 3 * (m - n) + 1; i < m + n; i += 2) {
          cout << 10;
        }
      } else {
        if (m - 1 == 2 * n) {
          cout << 1;
        } else {
          cout << 11;
        }
      }
    }
  }
}