#include <bits/stdc++.h>
using namespace std;
int d0, d1, t, res, a01, a00, a11, a10;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a00 >> a01 >> a10 >> a11;
  d0 = sqrt(a00 * 2) + 1;
  d1 = sqrt(a11 * 2) + 1;
  (d0 < d1 ? d0 : d1) -= (!a01 & !a10);
  if (d0 * (d0 - 1) != 2 * a00 || d1 * (d1 - 1) != 2 * a11 ||
      d0 * d1 != a10 + a01)
    cout << "Impossible";
  else {
    for (int i = d0 + d1; i >= 1; i--)
      if (a01 >= d1) {
        cout << 0;
        a01 = a01 - d1;
      } else {
        cout << 1;
        d1--;
      }
  }
  return 0;
}

### Prompt

Generate 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 d0, d1, t, res, a01, a00, a11, a10;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a00 >> a01 >> a10 >> a11;
  d0 = sqrt(a00 * 2) + 1;
  d1 = sqrt(a11 * 2) + 1;
  (d0 < d1 ? d0 : d1) -= (!a01 & !a10);
  if (d0 * (d0 - 1) != 2 * a00 || d1 * (d1 - 1) != 2 * a11 ||
      d0 * d1 != a10 + a01)
    cout << "Impossible";
  else {
    for (int i = d0 + d1; i >= 1; i--)
      if (a01 >= d1) {
        cout << 0;
        a01 = a01 - d1;
      } else {
        cout << 1;
        d1--;
      }
  }
  return 0;
}

```