#include <bits/stdc++.h>
using namespace std;
int main() {
  int a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  int n1 = sqrt(2 * a00) + 1;
  int n2 = sqrt(2 * a11) + 1;
  (n1 < n2 ? n1 : n2) -= (!a01 && !a10);
  if ((n1 * (n1 - 1)) / 2 != a00 || (n2 * (n2 - 1)) / 2 != a11 ||
      n1 * n2 != a01 + a10) {
    cout << "Impossible";
  } else {
    for (int i = n1 + n2; i > 0; --i) {
      if (a01 >= n2) {
        cout << 0;
        a01 -= n2;
      } else {
        cout << 1;
        n2--;
      }
    }
  }
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

For each string s consisting of characters '0' and '1' one can define four integers a00, a01, a10 and a11, where axy is the number of subsequences of length 2 of the string s equal to the sequence {x, y}. 

In these problem you are given four integers a00, a01, a10, a11 and have to find any non-empty string s that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1 000 000.

Input

The only line of the input contains four non-negative integers a00, a01, a10 and a11. Each of them doesn't exceed 109.

Output

If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1 000 000.

Examples

Input

1 2 3 4


Output

Impossible


Input

1 2 2 1


Output

0110

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main() {
  int a00, a01, a10, a11;
  cin >> a00 >> a01 >> a10 >> a11;
  int n1 = sqrt(2 * a00) + 1;
  int n2 = sqrt(2 * a11) + 1;
  (n1 < n2 ? n1 : n2) -= (!a01 && !a10);
  if ((n1 * (n1 - 1)) / 2 != a00 || (n2 * (n2 - 1)) / 2 != a11 ||
      n1 * n2 != a01 + a10) {
    cout << "Impossible";
  } else {
    for (int i = n1 + n2; i > 0; --i) {
      if (a01 >= n2) {
        cout << 0;
        a01 -= n2;
      } else {
        cout << 1;
        n2--;
      }
    }
  }
  return 0;
}

```