#include <bits/stdc++.h>
using namespace std;
char str[int(1e6) + 1];
int main() {
  long long xx, xy, yx, yy;
  cin >> xx >> xy >> yx >> yy;
  long long dx = sqrt(8 * xx + 1), dy = sqrt(8 * yy + 1);
  long long cx = (xx != 0 || xy != 0 || yx != 0 ? (1 + dx) / 2 : 0),
            cy = (yy != 0 || xy != 0 || yx != 0 ? (1 + dy) / 2 : 0),
            len = cy + cx;
  str[len] = 0;
  if (xx == 0 && yy == 0 && xy == 0 && yx == 0) {
    cout << 0;
    return 0;
  }
  if (cx * cy != xy + yx || cx + cy > 1000000 || sqrt(8 * xx + 1) - dx > 0.0 ||
      sqrt(8 * yy + 1) - dy > 0.0) {
    cout << "Impossible";
    return 0;
  }
  for (int i = 0; i < len; ++i) {
    if (xy >= cy) {
      str[i] = '0';
      xy -= cy;
      --cx;
    } else if (yx >= cx) {
      str[i] = '1';
      yx -= cx;
      --cy;
    } else {
      cout << "Impossible";
      return 0;
    }
  }
  cout << str;
  return 0;
}

### Prompt

Your challenge is to write 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;
char str[int(1e6) + 1];
int main() {
  long long xx, xy, yx, yy;
  cin >> xx >> xy >> yx >> yy;
  long long dx = sqrt(8 * xx + 1), dy = sqrt(8 * yy + 1);
  long long cx = (xx != 0 || xy != 0 || yx != 0 ? (1 + dx) / 2 : 0),
            cy = (yy != 0 || xy != 0 || yx != 0 ? (1 + dy) / 2 : 0),
            len = cy + cx;
  str[len] = 0;
  if (xx == 0 && yy == 0 && xy == 0 && yx == 0) {
    cout << 0;
    return 0;
  }
  if (cx * cy != xy + yx || cx + cy > 1000000 || sqrt(8 * xx + 1) - dx > 0.0 ||
      sqrt(8 * yy + 1) - dy > 0.0) {
    cout << "Impossible";
    return 0;
  }
  for (int i = 0; i < len; ++i) {
    if (xy >= cy) {
      str[i] = '0';
      xy -= cy;
      --cx;
    } else if (yx >= cx) {
      str[i] = '1';
      yx -= cx;
      --cy;
    } else {
      cout << "Impossible";
      return 0;
    }
  }
  cout << str;
  return 0;
}

```