#include <bits/stdc++.h>
using namespace std;
long long BS(int k) {
  long long lo = 0, hi = 1e9, md;
  while (hi >= lo) {
    md = (hi + lo) / 2;
    if (md * md - md == 2 * k)
      return md;
    else if (md * md - md > 2 * k)
      hi = md - 1;
    else
      lo = md + 1;
  }
  return -1;
}
int main() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  long long z = BS(a);
  long long o = BS(d);
  if (o == 0 && (c || b)) ++o;
  if (z == 0 && (c || b)) ++z;
  if (z == -1 || o == -1) {
    cout << "Impossible";
    return 0;
  }
  int x = z, y = o, q = c, w = b;
  ;
  string ans = "";
  for (int i = 0; i < z + o; ++i) {
    if (y && x <= q) {
      --y;
      q -= x;
      ans += '1';
    } else if (x && y <= w) {
      --x;
      w -= y;
      ans += '0';
    } else {
      cout << "Impossible";
      return 0;
    }
  }
  if (!a && !b && !c && !d)
    cout << 0;
  else if (w || q)
    cout << "Impossible";
  else
    cout << ans;
}

### Prompt

Please create a solution in CPP 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;
long long BS(int k) {
  long long lo = 0, hi = 1e9, md;
  while (hi >= lo) {
    md = (hi + lo) / 2;
    if (md * md - md == 2 * k)
      return md;
    else if (md * md - md > 2 * k)
      hi = md - 1;
    else
      lo = md + 1;
  }
  return -1;
}
int main() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  long long z = BS(a);
  long long o = BS(d);
  if (o == 0 && (c || b)) ++o;
  if (z == 0 && (c || b)) ++z;
  if (z == -1 || o == -1) {
    cout << "Impossible";
    return 0;
  }
  int x = z, y = o, q = c, w = b;
  ;
  string ans = "";
  for (int i = 0; i < z + o; ++i) {
    if (y && x <= q) {
      --y;
      q -= x;
      ans += '1';
    } else if (x && y <= w) {
      --x;
      w -= y;
      ans += '0';
    } else {
      cout << "Impossible";
      return 0;
    }
  }
  if (!a && !b && !c && !d)
    cout << 0;
  else if (w || q)
    cout << "Impossible";
  else
    cout << ans;
}

```