#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  ;
  int a1, a2, a3, a4;
  cin >> a1 >> a2 >> a3 >> a4;
  int s0, s1;
  bool flag = 1;
  int tmp = sqrt(a1 * 2 + 0.5);
  if (tmp * (tmp + 1) / 2 == a1)
    s0 = tmp + 1;
  else
    flag = 0;
  tmp = sqrt(a4 * 2 + 0.5);
  if (tmp * (tmp + 1) / 2 == a4)
    s1 = tmp + 1;
  else
    flag = 0;
  if (flag == 0) {
    cout << "Impossible" << endl;
    return 0;
  }
  if (a2 == 0 && a3 == 0) {
    if (a1 == 0) {
      for (int j = 1; j <= s1; ++j) cout << '1';
      cout << endl;
      return 0;
    } else if (a4 == 0) {
      for (int j = 1; j <= s0; ++j) cout << '0';
      cout << endl;
      return 0;
    }
  }
  if (s0 * s1 != a2 + a3) {
    cout << "Impossible" << endl;
    return 0;
  }
  while (a2 >= s1) {
    a2 -= s1;
    cout << '0';
    --s0;
  }
  tmp = s1 - a2;
  for (int j = 1; j <= tmp; ++j) cout << '1';
  if (s0 > 0) {
    cout << '0';
    --s0;
  }
  for (int j = tmp + 1; j <= s1; ++j) cout << '1';
  while (s0 > 0) {
    cout << '0';
    --s0;
  }
  cout << endl;
  return 0;
}

### Prompt

Please provide a CPP coded solution 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 main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  ;
  int a1, a2, a3, a4;
  cin >> a1 >> a2 >> a3 >> a4;
  int s0, s1;
  bool flag = 1;
  int tmp = sqrt(a1 * 2 + 0.5);
  if (tmp * (tmp + 1) / 2 == a1)
    s0 = tmp + 1;
  else
    flag = 0;
  tmp = sqrt(a4 * 2 + 0.5);
  if (tmp * (tmp + 1) / 2 == a4)
    s1 = tmp + 1;
  else
    flag = 0;
  if (flag == 0) {
    cout << "Impossible" << endl;
    return 0;
  }
  if (a2 == 0 && a3 == 0) {
    if (a1 == 0) {
      for (int j = 1; j <= s1; ++j) cout << '1';
      cout << endl;
      return 0;
    } else if (a4 == 0) {
      for (int j = 1; j <= s0; ++j) cout << '0';
      cout << endl;
      return 0;
    }
  }
  if (s0 * s1 != a2 + a3) {
    cout << "Impossible" << endl;
    return 0;
  }
  while (a2 >= s1) {
    a2 -= s1;
    cout << '0';
    --s0;
  }
  tmp = s1 - a2;
  for (int j = 1; j <= tmp; ++j) cout << '1';
  if (s0 > 0) {
    cout << '0';
    --s0;
  }
  for (int j = tmp + 1; j <= s1; ++j) cout << '1';
  while (s0 > 0) {
    cout << '0';
    --s0;
  }
  cout << endl;
  return 0;
}

```