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

### Prompt

Develop a solution in cpp to the problem described below:

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 a00, a01, a10, a11;
int n1, n2, i;
int main() {
  cin >> a00 >> a01 >> a10 >> a11;
  n1 = sqrt(2 * a00) + 1;
  n2 = sqrt(2 * a11) + 1;
  (n1 < n2 ? n1 : n2) -= (!a10 and !a01);
  if (n1 * (n1 - 1) != 2 * a00 or n2 * (n2 - 1) != 2 * a11 or
      a01 + a10 != n1 * n2)
    cout << "Impossible";
  else {
    for (i = n1 + n2; i > 0; i--) {
      if (a01 >= n2)
        cout << 0, a01 -= n2;
      else
        cout << 1, n2--;
    }
  }
}

```