#include <bits/stdc++.h>
using namespace std;
long long a, b, c, d, o, oo, i, ii, sh;
int main() {
  cin >> a >> b >> c >> d;
  while (sh < a) {
    sh += o;
    o++;
  }
  if (sh != a) {
    cout << "Impossible";
    return 0;
  }
  sh = 0;
  while (sh < d) {
    sh += i;
    i++;
  }
  if (sh != d) {
    cout << "Impossible";
    return 0;
  }
  if (i == 0 && (b != 0 || c != 0)) i = 1;
  if (o == 0 && (i == 0 || (b != 0 || c != 0))) o = 1;
  if (b + c != i * o) {
    cout << "Impossible";
    return 0;
  }
  while (i + o > 0) {
    if (b >= i) {
      cout << 0;
      b -= i;
      o--;
    } else {
      cout << 1;
      i--;
    }
  }
}

### 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 a, b, c, d, o, oo, i, ii, sh;
int main() {
  cin >> a >> b >> c >> d;
  while (sh < a) {
    sh += o;
    o++;
  }
  if (sh != a) {
    cout << "Impossible";
    return 0;
  }
  sh = 0;
  while (sh < d) {
    sh += i;
    i++;
  }
  if (sh != d) {
    cout << "Impossible";
    return 0;
  }
  if (i == 0 && (b != 0 || c != 0)) i = 1;
  if (o == 0 && (i == 0 || (b != 0 || c != 0))) o = 1;
  if (b + c != i * o) {
    cout << "Impossible";
    return 0;
  }
  while (i + o > 0) {
    if (b >= i) {
      cout << 0;
      b -= i;
      o--;
    } else {
      cout << 1;
      i--;
    }
  }
}

```